OGS Rank: Looking for an explanation

Short version:
Kyu and dan are like grades
25 kyu being the weakest recognised grade, goes up to 1 kyu, then 1 dan comes next and goes up to 9 dan.
In theory, each grade difference should closely map to 1 handicap stone on a 19x19 board.
The bigger numbers are glicko rating points, which are similar to elo. Bigger = stronger.
You can read more about that here: