What is meant by prostrating a great deal in the hadith “Help me to do that for you by prostrating a great deal”?

Firstly: 

With regard to the hadith referred to in the question, there is a proven report with a similar meaning, but not the same wording, from Rabee‘ah ibn Ka‘b al-Aslami (may Allah be pleased with him), who said: I used to stay overnight with the Messenger of Allah (blessings and peace of Allah be upon him) and bring him water for wudoo’ and whatever he needed. He said to me: “Ask.” I said: I ask to be with you in Paradise. He said: “Is there anything else?” I said: That is all. He said: “Help me to do that for you by prostrating a great deal.”

Narrated by Muslim in his Saheeh (489).

Imam an-Nawawi (may Allah have mercy on him) said:  

This shows that it is encouraged to prostrate a great deal; what is referred to here is prostration in prayer.

End quote from Sharh Muslim (4/206) 

The words of the Prophet (blessings and peace of Allah be upon him), “… by prostrating a great deal” are to be understood within the framework of the basic principle governing many of the Prophetic hadiths that connect rewards to actions, which is that whoever does more, Allah will add more to his reward, and whoever falls short will attain reward commensurate with what he does. Whoever does more, Allah, may He be glorified and exalted, will give him more and more, as one of the Sahaabah said to the Prophet (blessings and peace of Allah be upon him): Then we will do more. The Prophet (blessings and peace of Allah be upon him) said: “Then Allah will give more.”

Narrated by at-Tirmidhi, no. 3573. He said: It is hasan saheeh ghareeb with this isnaad. It was classed as saheeh by al-Albaani in Saheeh al-Adab al-Mufrad, no. 550 

Hence we say to the questioner here: the more you adhere to regularly offering the obligatory prayers on time, and the more you do naafil (supererogatory) prayers by night and day, the greater your chances of being with the Prophet (blessings and peace of Allah be upon him), and you will be with him in Paradise for longer. Whoever offers whatever he can of voluntary and naafil prayers will attain the honour of accompanying the Prophet (blessings and peace of Allah be upon him), in sha Allah, to a degree commensurate with that. Accompanying the Prophet (blessings and peace of Allah be upon him) is of varying degrees. Some of the people will accompany him constantly and will be with him all the time in Paradise; some of the people will have the joy of meeting him or seeing him, according to the level of their righteous deeds. 

This is what we understand from the hadith that was proven from Mi‘daan ibn Abi Talhah, who said: I met Thawbaan, the freed slave of the Messenger of Allah (blessings and peace of Allah be upon him) and said: Tell me of a deed that I may do, by which Allah may admit me to Paradise – or he said: Tell me of the most beloved of deeds to Allah. He remained silent. I asked him (again) and he remained silent. I asked him a third time and he said: I asked the Messenger of Allah (blessings and peace of Allah be upon him) about that and he said: “You should prostrate to Allah a great deal, for you will not perform one prostration to Allah but Allah will raise you one degree in status thereby and erase one sin for you.”

Narrated by Muslim in his Saheeh (488). 

Look at how the raising of degrees is commensurate with offering more prayers before Allah, may He be glorified and exalted, exactly as we understand from the words of Allah, may He be glorified and exalted (interpretation of the meaning):

“And whoso obeys Allah and the Messenger (Muhammad (blessings and peace of Allah be upon him)), then they will be in the company of those on whom Allah has bestowed His Grace, of the Prophets, the Siddiqoon (those followers of the Prophets who were first and foremost to believe in them, like Abu Bakr As-Siddiq), the martyrs, and the righteous. And how excellent these companions are!”

[an-Nisa’ 4:69].

It was narrated from Anas (may Allah be pleased with him) that a man asked the Prophet (blessings and peace of Allah be upon him) about the Hour. He said: When will the Hour be? He said: “What have you prepared for it?” He said: Nothing, except that I love Allah and His Messenger (blessings and peace of Allah be upon him). He said: “You will be with those whom you love.” Anas said: We did not rejoice over anything as we did over these words of the Prophet (blessings and peace of Allah be upon him): “You will be with those whom you love.” Anas said: I love the Prophet (blessings and peace of Allah be upon him), and Abu Bakr and ‘Umar, and I hope that I will be with them because of my love for them, even if I do not do what they did.

Narrated by al-Bukhaari (368) and Muslim (2639) 

So being with the Prophets and the martyrs is connected to obedience to Allah and His Messenger. The more acts of obedience one does and the more one loves Allah and His Messenger, the greater the reward will be of being with the righteous, and the closer one will be to the noble Messenger Muhammad (blessings and peace of Allah be upon him) in Paradise. 

Something similar may be said of all the deeds of which the reward is accompanying the Prophet (blessings and peace of Allah be upon him), such as sponsoring orphans, taking care of daughters and looking after them, and having a good attitude, as the Prophet (blessings and peace of Allah be upon him) said: “Among the most beloved of you to me and the most closely seated to me on the Day of Resurrection will be those of you who are best in attitude. Narrated by at-Tirmidhi (2018); he said: It is hasan ghareeb. It was classed as saheeh by al-Albaani in Saheeh at-Tirmidhi. This is a hadith which clearly states that the degree of closeness to the Prophet (blessings and peace of Allah be upon him) in Paradise will vary according to how good one’s attitude is. 

Shaykh ‘Abd al-Kareem al-Khudayr (may Allah preserve him) said: 

This indicates that there is no set number of voluntary rak‘ahs that one may do in naafil prayers by night or day; there is no set number: “Help me to do that for you by prostrating a great deal”. The more one does, the more likely it is that he will attain what he aspires to.

End quote from Sharh al-Muharrir fi’l-Hadith (27/11) 

Similarly, the more the prostration is characterised by proper focus and humility before Allah, the greater will be the reward and the closer one will become to Allah, may He be glorified and exalted, and to achieving nearness to the Prophet (blessings and peace of Allah be upon him) in Paradise. 

Shaykh al-Islam Ibn Taymiyah (may Allah have mercy on him) said: 

If one of the two prostrations is better than the other, then the rise in status thereby will be greater, and the amount of sin erased thereby will be greater. Just as the prostration in which one attains greater focus and presence of mind is superior to others, so too the lengthy prostration in which one is sincerely devoted to one’s Lord is superior to that which is shorter. 

We cannot say that what is greater in number but brief is better than what is fewer in number but done more properly and is longer, because the Prophet (blessings and peace of Allah be upon him) used to pray lengthy rak‘ahs.

End quote from Majmoo‘ al-Fataawa (23/78) 

We have previously discussed how some of the scholars quoted this hadith as evidence for the difference between prostration or standing, and which of them is greater in reward. Please see the answer to question no. 41857

And Allah knows best.