Ruling on Seeking Help from Other Than Allah
Question

I often hear people saying “Madad ya Rasul-Allah, Madad ya Sayyidina Al-Husayn, madad ya Sayyid ya Badawi…” and I do not know the meaning of these words.
Praise be to Allah.Avoiding unlawful acts of worship in Islam
It should be noted that Allah has created the universe to worship Him and Him alone. Allah says (interpretation of the meaning): 
“And I (Allah) created not the jinn and mankind except that they should worship Me (Alone).” [Adh-Dhariyat 51:56]
Allah sent the Messengers to call their people to worship Allah alone (Tawhid ) and to forbid them to associate anything with Him (polytheism). Allah says (interpretation of the meaning): 
“And We did not send any Messenger before you (O Muhammad) but We revealed to him (saying): La ilaha illa Ana [none has the right to be worshipped but I (Allah)], so worship Me (Alone and none else).” [Al-Anbiya’ 21:25]
What is Shirk?
Polytheism means directing worship to other than Allah, and Du`a comes under the heading of worship which must be devoted to Allah alone and not directed to anyone else. Hence the Prophet (peace and blessings of Allah be upon him) said: “Du`a is worship .” (Narrated by At-Tirmidhi, 2969; classed as authentic by Al-Albani in Sahih At-Tirmidhi) 
Can we seek help from other than Allah?
Asking for Madad (help or support) from anyone other than Allah, as mentioned in the question, is a kind of calling upon (or making Du`a to) someone other than Allah, hence it is a kind of polytheism. 
It says in Fatawa Al-Lajnah Ad-Da’imah (2/193): 
“The words of some of those who sing Nashid, “Madad ya sayyidina Al-Husayn (Help O our master Al-Husayn), Madad ya Sayyidah Zaynab, madad ya Badawi ya Shaykh Al-`Arab, madad ya Rasul Allah (O Messenger of Allah), Madad ya awliya’ Allah (O close friends – or ‘saints’ – of Allah),” etc, is major polytheism which puts the one who says it beyond the pale of Islam (Allah forbid), because it is calling upon the dead to give them good things, to help them, to ward off danger or relieve them of harm. That is because what is meant by madad is giving, help and support. So it is as if the person who says, “Madad ya Sayyid ya Badawi, madad ya Sayyidah Zaynab” etc is saying: Help us and give us of your bounty, and relieve us of hardship and ward off calamity from us. This is major polytheism. Allah says, after explaining to His slaves that He is in control of the universe and that it is subjugated to Him:
“Such is Allah, your Lord; His is the kingdom. And those, whom you invoke or call upon instead of Him, own not even a Qitmir (the thin membrane over the date stone).
If you invoke (or call upon) them, they hear not your call; and if (in case) they were to hear, they could not grant it (your request) to you. And on the Day of Resurrection, they will disown your worshipping them. And none can inform you (O Muhammad) like Him Who is the All-Knower (of everything).” [Fatir 35:13-14 – interpretation of the meaning] 
So He calls their prayers to others Polytheism. 
And Allah says (interpretation of the meaning): 
“And who is more astray than one who calls on (invokes) besides Allah, such as will not answer him till the Day of Resurrection, and who are (even) unaware of their calls (invocations) to them?
And when mankind are gathered (on the Day of Resurrection), they (false deities) will become their enemies and will deny their worshipping.” [Al-Ahqaf 46:6] 
So Allah tells us that those who are called upon other than Him, the Prophets and the righteous, are unaware of the call of those who call upon them and will never respond to their calls, and they will be their enemies and will deny their worship of them.  
And Allah says (interpretation of the meaning): 
“Do they attribute as partners to Allah those who created nothing but they themselves are created? No help can they give them, nor can they help themselves. And if you call them to guidance, they follow you not. It is the same for you whether you call them or you keep silent. Verily, those whom you call upon besides Allah are slaves like you. So call upon them and let them answer you if you are truthful.” [Al-A`raf 7:191-194] 
“And whoever invokes (or worships), besides Allah, any other Ilah (god), of whom he has no proof; then his reckoning is only with his Lord. Surely, Al-Kafirun (the disbelievers in Allah and in the Oneness of Allah, polytheists, pagans, idolaters) will not be successful.” [Al-Mu’minun 23:117]
So Allah tells us that whoever calls upon anyone other than Allah, among the dead etc., will never succeed because of his disbelief and his calling upon someone other than Allah.
For more details, please see the following answers: 181206 , 200862 , 2742 , 201175 , 220340 , 9918 , and 31807 .  
And Allah knows best.