This surah was revealed at the same time as the previous surah (al-Falaq). The prophet used to refer to them as al mu'awwidhatayn (verses of refuge) for obvious reasons. 

Notice how in Surat-ul-Falaq we call upon Allah one time (the Lord of al falaq) to seek his protection against 3 evils while in this surah we call upon Him 3 times (the Lord of mankind, the master of mankind, the God of mankind) to ask His protection against one evil (the whispering of shaytan). This tells us how dangerous the whispering is. The evil whisperer never gives up trying to lead us astray. The surah describes him as al-khannas, meaning he runs away when we remember and mention the name of Allah (especially by reciting this surah) then comes back during our times of weakness to try again. To accomplish this job, shaytan often uses clever disguises such as the media in our modern time.

The whispering is of two kinds: from shaytan (among jinn and humans as mentioned in the surah) and from within ourselves. Left uncontrolled and unsuppressed, the whispering from within ourselves could lead to disbelief.

There's a remarkable relationship between this surah (the last one) and surat-ul-faatiha (the first one). They both start with the mention of the Lordship of Allah, then they declare Him as the master and the ilah (the only one worthy of worship) before asking his assistance to guide us to the straight path (in faatiha) which necessitates protection from the whispering of shaytan (in this surah). So it's not surprising that every time our prophet would complete the recitation of the Qur'an (with this surah), he would immediately continue on to the beginning (with surat-ul-faatiha). It's as if one is never done with the Qur'an.