How is ‘Umrah in Ramadan Equivalent to Hajj?
Question

‘Umrah in the month of Ramadan is equivalent to Hajj. What is meant by that? I would like a detailed explanation.
Praise be to Allah.Hadith about ‘Umrah in Ramadan
Al-Bukhari (1782) and Muslim (1256) narrated that Ibn 'Abbas said: The Messenger of Allah (peace and blessings of Allah be upon him) said to a woman from among the Ansar – Ibn ‘Abbas mentioned her name but I forgot it – “What kept you from performing Hajj with us?” She said: We only have two camels and the father of her son and her son had gone for Hajj on one camel, and he left us the other camel so that we could carry water on it. He said: “When Ramadan comes, go for ‘Umrah , for ‘Umrah in (that month) is equivalent to Hajj.” 
Who attains the virtue of ‘Umrah in Ramadan?
The scholars differed concerning the one who attains the virtue of ‘Umrah in Ramadan. There are three opinions:  

That this hadith applies only to the woman who was addressed by the Prophet (peace and blessings of Allah be upon him). Among those who favoured this view was Sa’id ibn Jubayr among the Tabi’in, as was narrated from him by Ibn Hajar in Fath al-Bari (3/605). Among the evidence quoted in support of this view is the hadith of Umm Ma’qil who said: Hajj is Hajj and ‘Umrah is ‘Umrah. The Messenger of Allah (peace and blessings of Allah be upon him) said this to me and I do not know whether it was just for me or for all people. (Narrated by Abu Dawud (1989), but this version is da’if (weak); it was classed as such by al-Albani in Da’if Abi Dawud) 
That this virtue is attained by the one who intends to do Hajj but is unable to do it, then he makes up for it by doing ‘Umrah in Ramadan . For by combining the intention to do Hajj with performance of ‘Umrah in Ramadan, he attains the reward of doing a complete Hajj with the Prophet (peace and blessings of Allah be upon him). 

Ibn Rajab said in Lataif al-Ma’arif (p. 249). 
“It should be noted that the one who is unable to do a good deed and regrets that and wishes that he could do it will share the reward with the one who does it – and he mentioned a few examples of that – Some women missed out on doing Hajj with the Prophet (peace and blessings of Allah be upon him), and when he came they asked him about what would make up for that Hajj, and he said: “Do ‘Umrah in Ramadan, for ‘Umrah in Ramadan is equivalent to Hajj or to Hajj with me.” 
Ibn Kathir said something similar in his Tafsir (1/531). 
“This view was mentioned by Shaykh al-Islam Ibn Taymiyah as something possible in Majmu’ al-Fatawa (26/293-294).” 

The view of the scholars of the four madhhabs and others, that the virtue mentioned in this hadith is general in meaning and applies to everyone who does ‘Umrah in the month of Ramadan. ‘Umrah at that time is equivalent to Hajj for all people, not just for a few people or in certain circumstances. (See: Radd al-Muhtar (2/473); Mawahib al-Jalil (3/29); al-Majmu’ (7/138); al-Mughni (3/91); al-Mawsu’ah al-Fiqhiyyah (2/144) 

The most correct of these opinions – and Allah knows best – is the last one, and the virtue is general in meaning and is attained by all those who do ‘Umrah in Ramadan . This is indicated by the following: 

The hadith was narrated from a number of the Companions. Al-Tirmidhi said: Concerning this topic (reports were narrated) from Ibn 'Abbas, Jabir, Abu Hurayrah, Anas and Wahb ibn Khanbash. Most of the reports make no mention of the woman who asked the question.
The action of people throughout the ages, namely the Companions, Successsors, scholars and righteous people, who have always been eager to perform ‘Umrah in Ramadan so that they may attain this reward.

As for the idea that the virtue could only be attained by one who was unable to perform Hajj that year because of some impediment, it may be said that if a person sincerely intended and resolved to do Hajj, and took the appropriate means, then was prevented by something that was beyond his control, then Allah will decree the reward for that action because of his intention. So how could the Prophet (peace and blessings of Allah be upon him) make the reward conditional upon doing some additional action, namely performing ‘Umrah in Ramadan, when the sincere intention is sufficient to attain the reward? 
Meaning of ‘Umrah in Ramadan is equivalent to Hajj 
There remains the question about what is meant by the virtue mentioned, and that ‘Umrah in Ramadan is equivalent to Hajj. That may be explained as follows: 
Undoubtedly, ‘Umrah in Ramadan does not take the place of the obligatory Hajj, i.e., the one who does ‘Umrah in Ramadan has not discharged the duty to perform the obligatory Hajj for the sake of Allah. 
What is meant by the hadith is that they are alike in terms of reward, not in terms of fulfilling the duty. 
Nevertheless, what is meant by equivalency between the reward for ‘Umrah in Ramadan and the reward for Hajj is equivalency in terms of amount, not in terms of type. Undoubtedly Hajj is superior to ‘Umrah in terms of the type of action.  
The one who does ‘Umrah in Ramadan will attain a reward equal in amount to that of Hajj, but the action of Hajj brings special virtues and status that are not present in ‘Umrah, such as du’a in ‘Arafah, stoning the jamarat, offering the sacrifice and so on. Although they are equal in terms of the amount – or number – of reward, they are not equal in terms of type or nature. 
Ibn Taymiyah said something similar when he spoke about the hadith which says that Surat al-Ikhlas is equivalent to one third of the Quran. 
Ishaq ibn Rahawayh said: 
“What this hadith, i.e., “‘Umrah in Ramadan is equivalent to Hajj”, means is similar to the report narrated from the Prophet (peace and blessings of Allah be upon him) in which he said: “Whoever recites Qul Huwa Allahu Ahad has recited one third of the Quran.” (Sunan al-Tirmidhi, 2/268)  
In Masail al-Imam Ahmad ibn Hanbal (1/553) there is a report from Abu Ya'qub al-Kusaj: 
"I said: Who said “‘Umrah in Ramadan is equivalent to Hajj”? Is that proven? He said: Yes, it is proven. 
Ishaq said: “It is proven as he said. What it means is that there will be recorded for him a reward like that of Hajj, but he will never be like the one who performed Hajj at all.” 
Ibn Taymiyah said in Majmu’ al-Fatawa (26/293-294): 
“It is well known that what is meant is that your ‘Umrah in Ramadan is equivalent to Hajj with me, because she wanted to do Hajj with him but was not able to. So he told her what would take the place of that. The same applied to others among the Companions who were in the same position as her. No wise man would say what some ignorant people think, that the ‘Umrah of one of us from the miqat or from Makkah is equivalent to Hajj with him, because it is obvious that a complete Hajj is better than ‘Umrah in Ramadan, and even if one of us does the obligatory Hajj it cannot be like Hajj with him, so how can ‘Umrah be like that? The most that can be understood from the hadith is that the ‘Umrah of one of us from the miqat in Ramadan is equivalent to Hajj.”
And Allah knows best.