The other source of shari'ah. Just as muslims beleve that the Qur'an is the word of God. We believe that the hadith, and hence the sunnah are the words of the prophet Muhammad (Peace be upon him). Although there are many rules and advices mentioned in the Qur'an, most of them are vague. The sunnah is where they are explained.

Any verse that is not straight forward in it's meaning is explained in the hadith. Except for, of course, the muqatta'at. But then again, I guess you can even say that technically the muqatta'at are explained as well. I would rather say that they are mentioned. In addition to the explaination of verses in the Qur'an, the sunnah also contains additional rulings, additional forms of worship and explanations of both that which is contained in the Qur'an and the sunnah.

The sunnah is a very vaste topic. It is also the most widely studied Islamic science. The sunnah of Muhammad (Peace be upon him) is probably the most widely documented topic in the world.

Depending on your madhaab, or lack there of, the sunnah breaks down into 5 levels.
Fard: Technically not a sunnah, but included for the sake of completeness. That which is fard is obligatory due to it's being mentioned in the Quran. To refrain from such an act is a sin. Examples of that which is fard: zakat, salah, fasting the month of Ramadan.

Wajib:That which is wajib is obligatory due to the fact that it was ordered by the prophet Muhammad (Peace be upon him). To refrain from such an act is also a sin. Wajib exists in order to make a distinction, in a single word, between that which Allah ordered, and that which the prophet (peace be upon him) ordered. Examples of that which is wajib: For a muslim man, the growing of the beard and to make salat-ul-jummah in the mosque. For both men and women, salat-ul-witr.

Sunnah Muakadah: That which is compulsory. I think this comes about due to the fact that the prophet never left such an action, but he didn't order others to due it. To refrain from such an act on a continuous basis would be a sin, but there is no sin in leaving it seldomly. Example of that which is sunnah muakadah: 4 rakat of salah before the afternoon prayer, attending the masjid for the daily prayers.

Sunnah Ghair-Muakadah: That which is not compulsory and can be left without getting any sin, but it is still a good idea to do it. 4 rakah before salat-ul-asr is an example of this.

Nafil: That which is recommended. There is also no sin for leaving this action. Many things fall under this category. Most of the fasting that is done outside of Ramadan fall under this category.

JFYI, the sunna circumcision is not sunnah, it is haram.