The Qur'an is the last divine book, which was revealed from Allah as a declaration and guidance to mankind. It is an explanation of all things and means for men to be rightly guided. In many verses of the Qur'an, it is commanded to obey the prophet of Allah. This is quite a significant point because understanding the Qur'an fully can only be possible with following the Sunnah of the prophet.
The Sunnah is the explanation of the Qur'an. It is the creed of ahl-i Sunnah, which has been constituted with collecting true hadiths of the prophet Muhammad (sallallahu `alayhi wa sallam), and interpretation of these hadiths by great scholars in later times.
It's worth dwelling upon a point here. The Sunnah is not a concept that can be dealt with separately from the Qur'an. In the Qur'an, it has been mentioned that the prophet removes heavy burdens, makes rules, teaches the ummah (society) the open and hidden meanings of the Qur'an.
As a matter of fact, when we look at the practices of Sunnah, we see that the prophet of Allah gave His companions a lot of information about numerous subjects. This information was then interpreted by scholars of the time, continued to be practised in daily lives and has passed on to us generations to generations.
Allah has informed in the surah Al-e Imran that the Prophet had the characteristic of teaching the Qur'an and purifying mankind:
Certainly Allah conferred a benefit upon the believers when He raised among them a Messenger from among themselves, reciting to them His communications and purifying them, and teaching them the Book and the wisdom, although before that they were surely in manifest error. (Surah Al-e Imran, 164)