X-square: the corner opens along the diagonal
If you play on the X-square diagonally next to an empty corner, the opponent can often reach the corner along that diagonal. It is the most common way to give away a corner.
Exception: giving up a corner to set up a wedge
On the other hand, the next exercise is a position from a different game. After Black G2, White took H1, but if Black wedges in at G1, the white discs on B1 to F1 sit between Black G1 and the empty A1. Black can then aim at the A1 corner. In cases like this, compare what you gain for the corner you give up, together with the whole position.
Exercise
After Black G2, White took the H1 corner. Black to move. Where on the top edge should Black wedge in to make a foothold aiming at the A1 corner?
C-square: dangerous when the squares next to it are empty
A C-square can also lead to losing a corner. Be especially careful with a lone C-square: the corner and A-square next to it are empty, and it is cut off from the other discs on the edge. The opponent can play next to it on the A-square and make a foothold that traps the C-square disc. With your own discs connected along the edge you can sometimes defend, but you have to check the opponent's actual legal moves and replies.