The outer lines of the board are called edges. A disc on an edge can only be trapped along the edge, so it is flipped less often than a disc in the middle.
Among them, a disc that no move can ever flip again is called a stable disc. A corner is stable by itself, and discs of the same color connected to a corner along an edge without gaps are stable too.
Stable discs are certainly yours until the end of the game. That is the biggest reason corners matter. Later you will also learn that in the middle of the game, the number of moves you can play matters more than the number of discs.