Dan and Kyu ranks

Dan and kyu are ranks indicating your strength.
These ranks are the same as in the martial arts, like Judo.
The higher the dan, the stronger a player is, but the lower the kyu the stronger.

Amateur rank Professional rank
8-dan 9-dan
7-dan 8-dan
6-dan 7-dan
5-dan 6-dan
4-dan 5-dan
3-dan 4-dan
2-dan 3-dan
1-dan 2-dan
1-kyu 1-dan

Professional ranks go from 1-dan to 9-dan, but these are incomparably stronger than amateur ranks.
Amateur starts at 25-kyu and go up to 8-dan. If you understand atari, you are 25-kyu.
The Nihon ki-in issues diplomas attesting to strength ingo.
The great thing about Go is that people of different strength can enjoy playing each other by using the handicap system. In general, the handicap is one stone for each dan or kyu difference in rank.