Praise be to Allah.

Allah, may He be exalted, offered obedience to Him and His obligations and limits to the heavens and the earth and the mountains in such a way that if they did well they would be rewarded, but if they neglected their duties they would be punished. They refused to bear it out of fear that they might not do what was enjoined upon them, but man took it on, and verily he was unjust (to himself) and ignorant (of its results). 

This is the explanation of the verse in which Allah, may He be glorified and exalted, says: “Truly, We did offer al-amaanah (the trust or moral responsibility or honesty and all the duties which Allah has ordained) to the heavens and the earth, and the mountains, but they declined to bear it and were afraid of it (i.e. afraid of Allah’s torment). But man bore it. Verily, he was unjust (to himself) and ignorant (of its results) [al-Ahzaab 33:72]”. 

The interpretation of the amaanah (trust) as referring to shar‘i duties is the view of Ibn ‘Abbaas, al-Hasan al-Basri, Mujaahid, Sa‘eed ibn Jubayr, ad-Dahhaak ibn Muzaahim, Ibn Zayd and most of the commentators. 

See: Tafseer at-Tabari, 20/336-340; Tafseer Ibn Katheer, 6/488-489; al-Jaami‘ li Ahkaam al-Qur’an, 14/252-253; Fath al-Qadeer, 4/437. 

Qataadah said: The amaanah (trust) is the religion, obligatory duties and limits set by Allah. 

It was also said that what is meant by the amaanah here is whatever people entrust one with. 

Some of them said that it refers to ghusl in the case of janaabah. 

Zayd ibn Aslam said: The amaanah is three things: prayer, fasting and ghusl in the case of janaabah. 

Ibn Katheer (may Allah have mercy on him) said:

There is no contradiction between these opinions; rather they are all in harmony and refer to responsibility and accepting the commands and prohibitions on the basis of their condition, which is that if they do well they will be rewarded and if they neglect them they will be punished. Man accepted this amaanah despite his weakness, ignorance and injustice (to himself), except those who Allah guides. End quote. 

Tafseer Ibn Katheer, 6/489 

At-Tabari (may Allah have mercy on him) said:  

The most correct of these opinions is that of those who said that what is meant by the amaanah (trust) here is everything with which one is entrusted with regard to religious commitment and things entrusted to one by people. That is because Allah did not specify any particular type of trust when He said, “Truly, We did offer al-amaanah (the trust)”. End quote. 

Tafseer at-Tabari, 20/342 

Al-Qurtubi (may Allah have mercy on him) said: 

The word amaanah is general in meaning and encompasses all the duties of Islam, according to the correct opinion. This is the view of the majority. End quote. 

Al-Jaami‘ li Ahkaam al-Qur’an, 14/252 

As-Sa‘di (may Allah have mercy on him) said: 

Everything that Allah has enjoined upon His slave is an amaanah (trust), and the slave must carry them out in the fullest sense. That also includes things that are entrusted to one by people, such as wealth, secrets and the like. The individual must pay attention to both matters and fulfil both trusts. “Verily! Allah commands that you should render back the trusts to those, to whom they are due” [an-Nisa’ 4:58]. End quote. 

Tafseer as-Sa‘di, p. 547 

Ash-Shanqeeti (may Allah have mercy on him) said: 

In this verse Allah, may He be glorified and exalted, tells us that He offered the amaanah, which is the taking on of duties and the consequences of reward or punishment, to the heavens and the earth and the mountains, but they refused to bear it and were afraid of it. In other words, they were scared of the consequences of taking on this trust, lest that lead to the punishment and wrath of Allah. This offer, refusal and fear happened in a true sense. Allah created the heavens and the earth and the mountains with a sense of understanding, the nature of which only Allah knows and we do not know. Thus they understood when this trust was offered to them, and they refused and were afraid. End quote. 

Adwa’ al-Bayaan, 36/139 

To sum up: 

The amaanah (trust) mentioned in this verse, that Allah offered to the heavens and the earth and the mountains, but they refused to bear it and were afraid of it, but man took it on, is the Islamic duties, whether that has to do with duties towards Allah, may He be exalted, or duties towards His slaves. The one who fulfils his duty towards Allah and towards His slaves will be rewarded, but the one who neglects his duty towards Allah and towards His slaves deserves punishment. 

And Allah knows best.