Praise be to Allah.

Allah, may He be exalted, says in Soorat al-Maa’idah (interpretation of the meaning):

“O you who believe! Ask not about things which, if made plain to you, may cause you trouble. But if you ask about them while the Quran is being revealed, they will be made plain to you. Allah has forgiven that, and Allah is Oft-Forgiving, Most Forbearing”

[al-Maa’idah 5:101]. 

This verse forbade the believers to ask the Prophet (blessings and peace of Allah be upon him) about matters concerning which Allah had not said anything in His Book and had not said anything concerning them; splitting hairs and asking too many details about them might lead to them being prohibited, which would cause them hardship. It also forbade them to ask about things that were hidden from them and if they came to know about them it would upset them, such as how sound their attribution to their fathers was. 

That indeed happened. Al-Bukhaari (540) and Muslim (2359) narrated from Anas ibn Maalik that the Messenger of Allah (blessings and peace of Allah be upon him) came out when the sun had passed its zenith and led them in praying Zuhr. Then he stood on the minbar and spoke of the Hour, and said that momentous events would occur during it. Then he said: “Whoever would like to ask about anything, let him ask; you will not ask me about anything but I will tell you about it, so long as I am standing here.” The people wept a great deal, and he kept saying: “Ask me.” ‘Abdullah ibn Hudhaafah as-Sahmi stood up and said: Who is my father? He said: “Your father is Hudhaafah.” Then he kept saying, “Ask me.” Then ‘Umar knelt up and said: We are pleased with Allah as our Lord, Islam as our religion, and Muhammad as our Messenger. [The Messenger of Allah (blessings and peace of Allah be upon him)] fell silent, then he said: “Paradise and Hell were shown to me just now, on this wall, and I have never seen anything as good (as what I saw in Paradise) or anything as evil (as what I saw in Hell).” 

Imam Muslim (may Allah have mercy on him) said, after narrating this hadeeth: Ibn Shihaab said: ‘Ubaydullah ibn ‘Abdullah ibn ‘Utbah told me: Umm ‘Abdullah ibn Hudhaafah said to ‘Abdullah ibn Hudhaafah: I have never heard of a son more disrespectful to his parents than you. Could you be certain that your mother did not commit (immoral deeds) as some of the women of the Jaahiliyyah did, and thus you would expose her to scandal before the people? ‘Abdullah ibn Hudhaafah said: By Allah, if he had attributed me to a black slave, I would have accepted it. 

End quote from Saheeh Muslim (4/1832). 

Ash-Shawkaani (may Allah have mercy on him) said in his commentary on the verse in al-Maa’idah – “O you who believe! Ask not about things which, if made plain to you, may cause you trouble” –: That means: do not ask about things that you do not need to ask about and that are none of your concern in matters of your religion. The words “if made plain to you, may cause you trouble” are describing those things. In other words: do not ask about things of this nature, which if they were made plain to you and were made obligatory upon you, would cause you trouble. Allah forbade them to ask the Messenger of Allah (blessings and peace of Allah be upon him) a great deal, because asking about matters that do not concern one or that one does not need to know may be a cause of it being made obligatory upon the one who asks the question and others. The words “But if you ask about them while the Qur’an is being revealed, they will be made plain to you” also describe those things. What is meant is: do not ask about things, for if you ask about them whilst the Qur’an is being revealed, which is whilst the Messenger of Allah (blessings and peace of Allah be upon him) is still among you and the Revelation is still coming down to him, they will be made plain to you, i.e., they will be explained to you  by means of the answer that the Prophet (blessings and peace of Allah be upon him) gives you or what is enjoined upon you by the Revelation. Thus that will be a cause of hardship and of making obligatory something that was not obligatory, or of the prohibition of that which was not prohibited. This is unlike asking about things after the Revelation ceased with the death of the Messenger of Allah (blessings and peace of Allah be upon him), for then no obligations or prohibitions would come about because of asking.

End quote from Fath al-Qadeer by ash-Shawkaani (2/92). 

A number of things are known from this: 

Firstly: 

The prohibition mentioned in the verse applies specifically to the time of the Prophet (blessings and peace of Allah be upon him), which was the time when Revelation was still coming down, unlike times that came after that. Hence this does not mean that we should not seek Islamic knowledge and learn that which will benefit us or that we need to know with regard to matters of this life and the hereafter. 

Shaykh Ibn ‘Uthaymeen (may Allah have mercy on him) said:

it is truly unfortunate that some people say that you should not ask lest you be told of something that will cause you hardship, then they misinterpret the verse in which Allah, may He be exalted, says (interpretation of the meaning): “O you who believe! Ask not about things which, if made plain to you, may cause you trouble” [al-Maa’idah 5:101]. Rather the prohibition on asking was applicable only at the time when the Revelation was coming down, at which time it was possible that the rulings could be renewed or changed. But after the death of the Messenger of Allah (blessings and peace of Allah be upon him and his family), it is obligatory for the individual to ask about everything that he needs to know about matters of his religion.

End quote from Fataawa Noor ‘ala ad-Darb by Ibn ‘Uthaymeen (24/223) 

Secondly: 

The things that they were forbidden to ask about were: 

1.Things that had no bearing on their actions and were of no benefit in religious terms

2.Things that Islam said nothing about, out of mercy to people, not out of forgetfulness, because asking too many questions about that could lead to them being forbidden, which would cause hardship for people. Al-Bukhaari (6745) and Muslim (4349) narrated that Sa‘d ibn Abi Waqqaas (may Allah be pleased with him) said: The Messenger of Allah (blessings and peace of Allah be upon him) said: “One of the worst sins a Muslim could commit is asking about something that was not prohibited to the Muslims, but it became prohibited to them because of his asking.”

3.Things that were unknown to those who asked about them, which if they were made plain to them would cause them trouble, as we have seen above in the hadeeth of ‘Abdullah ibn Hudhaafah.

Thirdly: 

With regard to matters that are connected to the explanation of a shar‘i ruling, Allah has instructed us to ask about them, as He says (interpretation of the meaning):

“So ask those who possess knowledge if you do not know”

[an-Nahl 16:43]. 

Shaykh as-Sa‘di (may Allah have mercy on him) said in his commentary on the verse in al-Maa’idah:

Allah forbids His believing slaves to ask about things which, if they are made plain to them, will cause them trouble and grief, such as when some of the Muslims asked the Messenger of Allah (blessings and peace of Allah be upon him) about their fathers, or about their situation in Paradise or Hell. Perhaps if these matters were made plain to the one who asked, there would be nothing good for him in it. Another example is when they asked about things that had not happened, or they asked about things which would lead to stricter rulings in sharee‘ah that could cause hardship for the ummah, or they asked about matters that do not concern them. Asking about these and similar matters is what is forbidden. As for asking questions that will not result in any such thing, this is what is enjoined, as Allah, may He be exalted, says (interpretation of the meaning):

“So ask those who possess knowledge if you do not know”

[an-Nahl 16:43]. 

For more information on matters concerning which it is makrooh to ask, either in the sense of it being haram or discouraged, please see fatwa no. 131675.

And Allah knows best.