(who fear Allah without seeing Him) The address is to all human beings, whether they are believers or unbelievers. For the believer it contains the admonition that while living his life in the world he should always remember that not only his open and hidden deeds but even his secret intentions and innermost thoughts are not hidden from Allah; and for the unbeliever the warning that he may do whatever he may please fearless of God, but nothing that he does can remain un-noticed and unseen by Him.
Tafsir Ibn-Kathir: The Reward of those Who fear their Lord unseen
Allah informs of he who fears standing before his Lord, being frightened about matters between himself and Allah when he is not in the presence of other people. So he refrains from disobedience and he performs acts of obedience when no one sees him except Allah. Allah mentions that this person will have forgiveness and a great reward. This means that his sins will be remitted and he will be rewarded abundantly.
This is similar to what has been confirmed in the Two Sahihs:
(There are seven people whom Allah the Exalted will shade in the shade of His Throne on the Day when there will be no shade except its shade.) Then he mentioned that among those people are: (A man who is tempted by a beautiful woman of high social status, but he says: `Verily, I fear Allah.' Another person from among them is a man who gives charity and he conceals it so that his left hand does not know what his right hand spent.)
Muhammad Asad Explanation:
This is same as the opening of verse 3 of Surah Al Baqarah, wherein it is said: "who believe in [the existence of] that which is beyond the reach of human perception".
That is Al-ghayb (commonly, and erroneously, translated as "the Unseen") is used in the Qur'an to denote all those sectors or phases of reality which lie beyond the range of human perception and cannot, therefore, be proved or disproved by scientific observation or even adequately comprised within the accepted categories of speculative thought: as, for instance, the existence of God and of a definite purpose underlying the universe, life after death, the real nature of time, the existence of spiritual forces and their inter-action, and so forth. Only a person who is convinced that the ultimate reality comprises far more than our observable environment can attain to belief in God and, thus, to a belief that life has meaning and purpose. By pointing out that it is "a guidance for those who believe in the existence of that which is beyond human perception", the Qur'an says, in effect, that it will - of necessity - remain a closed book to all whose minds cannot accept this fundamental premise.
Yusuf Ali Explanation:
Read "unseen" adverbially. To fear the Lord is to love Him so intensely that you fear to do anything which is against His Will, and you do it because you realise Him intensely in your hearts, though you do not see Him with your bodily senses. Nor is it of any consequences whether other people see your love or the consequences that flow from your love, for your good deeds are for the love of Allah and not for show in the eyes of men. Such intensity of love obtains forgiveness for any past, and is indeed rewarded with Allah's love, which is immeasurably precious beyond any merits you may possess.
Javed Ahmad Ghamidi Explanation:
The implication is that these people comprehend their Lord through their vision and intellect and fear Him on this very basis. They do not insist on seeing Him and then believing in Him.