- Moving the Bishop to the square g4 or g5. I think that is a key idea.
- Developing a piece out of the opening
- In some cases, pinning an enemy knight to a queen with hopes to exploit a pin or at least try to induce weaknesses caused by opponents not reacting to the pin correctly.
- If g4/g5 are supported, lashing out at the enemy queen to force her to move or block by moving a piece to an undesirable square along the diagonal in between.
Note that all of the above except #1 are nuanced ideas that are based on the position at hand and may not even apply in some cases. There is no magic thumb-rule about Bg4/Bg5 (or any "piece on a certain square" chess move except castling!)
What is the main ideas behind the move Bg4 or Bg5 in chess games and its functions ?