Getting kicked from a server means the act of a responsible disconnecting a player from the server. This could be the result of a player using inappropriate language, discrimination, abuse, exploit, racism, severly hindering gameplay process, etc.
A player can get kicked by admin or by vote. When a player gets kicked, his client is disconnected from the server unwillingly. The player might reconnect immediately afterwards to the server to play again. You could consider a kick as a warning to prevent further bad behavior (which can lead to a ban).