Suppression is a mechanic that causes units to move 65% slower and greatly reduces reload speed for ranged weapons. There are only a few ways to break suppression, including, but not limited to retreating and using certain squad abilities(can be broken by Tactical Advance at the cost of speed (Tarkus' squad in Campaign)). Suppression can be caused from taking too much firepower whilst not in cover (mostly caused by Heavy Bolters (Avitus' squad in Campagin)), and other squad abilities(can be caused by Suppressing Fire(Cyrus' squad in Campaign)).
When squads are suppressed, their symbol blinks red, and the units are crouching. They also say things to let the player know that they are being suppressed, such as Tarkus (tactical marine squad) can be heard saying "Taking heavy fire!"