Referees frequently use their hands and body to signal calls like free kicks, offsides, and other decisions, whereas assistant referees communicates with the head referee and the players using their flags.
These signs must be understood not only by the referee, but also by the players. The full list of refereeing signals for the head referee and their deputy referees can be found here.
Here is the complete list of the signals by the head referee according to the Laws of the Game.
Advantage (Play on)
Hold a hand or both of your hands up (like in above images) so everyone can see you allowing advantage.
Direct Free Kick
Hold a hand up and point to defending goal.
Indirect Free Kick
Raise your hand up to indicate an indirect free kick.
Point to the corner arc using your hand.
Point your hand to the goal area of defending team.
Point your hand or your finger to the penalty mark.
Red & Yellow Card
Show the yellow or red card facing the player who is the card for.
Put finger(s) to ear, while extending the other arm/hand.
Draw a square box (TV) in the air using your hands/fingers.