A player is sent off when given a red card, immediately removed from play. Given for serious fouls, violent conduct, spitting, stopping a clear goal with a foul or handball, or getting a second yellow card. Your team plays the rest of the match a man down and can't replace you. Usually comes with a ban for future games too. Going down to 10 men is a major disadvantage, though some teams have won despite it.
How often a player is fit and can be selected. "The best ability is availability" is famously linked to NFL Hall of Fame Coach Bill Parcells, but it applies across all elite sport. Players who miss lots of games through injury affect squad planning, momentum, and results. Clubs now track injury history carefully in recruitment. Eden Hazard at Real Madrid is the cautionary tale - constantly injured, barely played.