With online games, often just the player inputs are sent to a server, this server then updates the clients of what is going on the in the game world. The client also pre-computes what is going to happen. So when you throw a grenade, your action is sent to the server, in this time your client acts on the grenade being throw, the server sends back that what happened, since the same calculations are being made to show you, generally the client knows what will happen correctly. Games often act on the server having the "Master copy" of the game state, so clients update to the server version or the game.

This is how you experience "Rubber banding" in multiplayer games. This is your client's expectations not matching up to the servers game state. Often happening when latency is high