What Is the Meaning of Tawhid?
Question

What is the meaning of Tawhid and what are its categories?
Praise be to Allah.What is tawhid?
Tawhid in Arabic means attributing Oneness to Allah and describing Him as being One and Unique, with no partner or peer in His Essence and Attributes.
The Arabs say wahid, ahad and wahid, all meaning one. Allah is Wahid, meaning that He has no rivals or peers in any way. So Tawhid means knowing Allah is One, with none like unto Him. Whoever does not acknowledge Allah in these terms and does not describe Him as being One with no partner or associate does not believe in Tawhid. 
Shar’i definition of Tawhid
With regard to the Shar’i definition of Tawhid, it means believing in Allah Alone as God and Lord and attributing to Him Alone all the attributes of Lordship and divinity.  
It may be defined as follows: Believing that Allah is One with no partner or associate in His Lordship (rububiyyah), divinity (uluhiyyah) or names and attributes (al-asma wa’l-sifat). 
This word (Tawhid) and its derivatives are used with this meaning in the Quran and Sunnah. For example: 
Allah says (interpretation of the meaning): 
“Say (O Muhammad): He is Allah, (the) One [Ahad]. Allah-us-Samad [Allah — the Self-Sufficient Master, Whom all creatures need, (He neither eats nor drinks)]. He begets not, nor was He begotten. And there is none co-equal or comparable unto Him” [al-Ikhlas 112:1-4]
“And your Ilah (God) is One Ilah [ilahun wahidun] (God — Allah), La Ilaha illa Huwa (there is none who has the right to be worshipped but He), the Most Gracious, the Most Merciful” [al-Baqarah 2:163]
“Surely, disbelievers are those who said: ‘Allah is the third of the three (in a Trinity).’ But there is no Ilah (god) (none who has the right to be worshipped) but One Ilah [ilahun wahidun] (God —Allah). And if they cease not from what they say, verily, a painful torment will befall on the disbelievers among them” [al-Maidah 5:73]
And there are many similar verses. 
In Sahih al-Bukhari (7372) and Sahih Muslim (19) it is narrated that Ibn ‘Abbas (may Allah be pleased with him) said: When the Prophet (peace and blessings of Allah be upon him) sent Mu’adh ibn Jabal to Yemen, he said to him: “You are going to people from among the People of the Book, so let the first thing to which you call them be belief in Allah alone (Tawhid). If they accept that, then tell them that Allah has enjoined on them five prayers every day and night. If they pray then tell them that Allah has enjoined on them zakah from their wealth to be taken from their rich and given to their poor. If they agree to that then take it from them but avoid the best of people’s wealth.”  
In Sahih Muslim it is narrated from Ibn ‘Umar (may Allah be pleased with him) that the Prophet (peace and blessings of Allah be upon him) said: “Islam is built on five (pillars) : belief that Allah is One, establishing regular prayer, paying zakah, fasting Ramadan and Hajj.” 
What is meant by Tawhid in all these texts is affirming the meaning of the testimony that there is no god but Allah and that Muhammad is the Messenger of Allah, which is the essence of the religion of Islam with which Allah sent His Prophet Muhammad (peace and blessings of Allah be upon him), based on the evidence of the words of the Quran and Sunnah. 
In some versions of the hadith of Muadh quoted above it says: “You will come to some people from among the People of the Book so when you come to them, call them to bear witness that there is no god except Allah and that Muhammad is the Messenger of Allah.” (Narrated by al-Bukhari, 1492)
According to another version of the hadith of Ibn ‘Umar: The Messenger of Allah (peace and blessings of Allah be upon him) said: “Islam is based on five (pillars): the testimony that there is no god except Allah and that Muhammad is His slave and Messenger...” (Narrated by Muslim, 16)
This indicates that Tawhid is the essence of the testimony that there is no god except Allah and that Muhammad is the Messenger of Allah, and that this is Islam with which Allah sent His Prophet to the two races of mankind and the jinn, other than which Allah will not accept any religion from anyone. 
Allah says (interpretation of the meaning): 
“Truly, the religion with Allah is Islam” [Al ‘Imran 3:19]
“And whoever seeks a religion other than Islam, it will never be accepted of him, and in the Hereafter he will be one of the losers” [Al ‘Imran 3:85]
Categories of Tawheed
Once this is understood, it should be noted that the scholars have divided Tawhid into three categories , as follows: 
Tawhid al-Rububiyyah (Oneness of Divine Lordship), Tawhid al-Uluhiyyah (Oneness of Divinity) and Tawhid al-Asma wa’l-Sifat (Oneness of the Divine Names and Attributes). 
What is Tawheed al-Rububiyyah?
Tawhid al-Rububiyyah (Oneness of Divine Lordship): means believing in Allah as One and Unique with regard to His actions such as creation, sovereignty, control, giving life and death, and so on.
There is a great deal of evidence to support this in the Quran and Sunnah. Please see question no. 13532  to learn some of it. 
Whoever believes that there is any creator other than Allah or any sovereign controlling this universe and disposing of its affairs other than Allah has denied this aspect of Tawhid and disbelieved in Allah. 
The kuffar of old accepted this aspect of Tawhid in general terms, although they differed with regard to some of its details. The evidence that they used to accept this is to be found in several verses of the Quran such as the following (interpretation of the meaning): 
“And if you were to ask them: ‘Who has created the heavens and the earth and subjected the sun and the moon?’ they will surely reply: ‘Allah.’ How then are they deviating (as polytheists and disbelievers)?” [al-'Ankabut 29:61] 
“And if you were to ask them: ‘Who sends down water (rain) from the sky, and gives life therewith to the earth after its death?’ they will surely reply: ‘Allah.’ Say: ‘All the praises and thanks be to Allah!’ Nay, most of them have no sense” [al-‘Ankabut 29:63] 
“And if you ask them who created them, they will surely say: ‘Allah.’ How then are they turned away (from the worship of Allah Who created them)?” [al-Zukhruf 43:87]
In these verses Allah states that the kuffar affirm that He is the Creator, Sovereign and Controller, but despite that they do not worship Him alone (Tawhid of worship), which points to the graveness of their wrongdoing and lies, and the weakness of their reasoning. For if there is One Who is described in such terms, none should be worshipped except Him Alone and none should be described as being one and unique except Him; may He be glorified above those that they associate with Him. 
So whoever affirms this Tawhid in the true sense must inevitably also affirm the Oneness of Allah’s Divinity (Tawhid al-Uluhiyyah). 
What is Tawheed al-Uluhiyyah?
Tawhid al-Uluhiyyah means devoting all acts of worship, both inward and outward, in word and deed, to Allah Alone, and not worshipping anything or anyone other than Allah, no matter who he is. Allah says (interpretation of the meaning): 
“And your Lord has decreed that you worship none but Him” [al-Isra 17:23] 
“Worship Allah and join none with Him (in worship)” [al-Nisa 4:36]
It may be described as devoting all one’s actions to Allah Alone.  
It is called Tawhid al-Uluhiyyah because it is based on ta-alluh lillah which is worship and devotion of Allah accompanied by love and veneration. 
It is also called Tawhid al-‘Ibadah (oneness of worship) because it means that a person worships Allah by doing what He has commanded and avoiding that which He has forbidden. 
It is also called Tawhid al-Talab wa’l-Qasd wa’l-Iradah (Oneness of goal, purpose and will) because it means that a person does not seek anything except the Face of Allah, so he worships Him sincerely. 
This is the kind of Tawhid concerning which people went astray, which is why the prophets were sent and the Books were revealed. This is the purpose for which the universe was created and laws were prescribed. Concerning this, disputes arose between the prophets and their peoples, so the stubborn were doomed and the believers were saved. 
Whoever goes astray with regard to this Tawhid, such as devoting some of his worship to someone other than Allah, has gone beyond the pale of Islam and drifted away from true belief. May Allah protect us from that.
What is Tawhid al-Asma wa’l-Sifat?
With regard to Tawhid al-Asma wa’l-Sifat (Oneness of the Divine Names and Attributes ), this means affirming the names and attributes of Allah and believing that there is none like unto Allah in His names and attributes. 
Principles of Tawhid al-Asma wa’l-Sifat
This Tawhid is based on two principles: 
1 – Affirmation: i.e., affirming that which Allah has affirmed for Himself in His Book or that His Prophet (peace and blessings of Allah be upon him) has affirmed of His beautiful names and sublime attributes in a manner that suits the Majesty and Greatness of Allah, without distorting them, twisting their meanings, denying their reality or discussing how they are. 
2 – Denial: i.e., denying that Allah has any faults and denying any shortcomings that He has denied Himself. The evidence for that is the words of Allah (interpretation of the meaning): 
“There is nothing like Him, and He is the All-Hearer, the All-Seer” [al-Shura 42:11]
So He has denied that He bears any resemblance to His creation, and affirmed that He has attributes of perfection in a manner that befits Him, may He be glorified.
References:
Al-Hujjah fi Bayan al-Mahajjah, 1/305.
Lawami’ al-Anwar al-Bahiyyah, 1/57.
And Allah knows best.