Lag is a term indicating the latency (i.e. tendency for delay) of a particular Internet connection.
More lag means a longer time is required for a player's moves to be communicated to the game server, which can make it seem as though the player is moving somewhat more slowly.
The difference is not usually very important for standard chess games, but can have a big effect on blitz and bullet games. Because of this, the game timer takes relative amounts of lag into consideration when determining how much time a player actually took to move.
Next to each player's name you will see several bars which show how good or bad that player's connection is:
Excellent Connection (very low lag), has full bars
OK Connection (some lag), has one or two fewer bars
Poor Connection (high lag) has one bar
Disconnected *If the bar turns RED and the clock is flashing, that means you are disconnected!*
The system will automatically compensate for some lag, up to a limit. If you notice that your opponent’s clock is moving up by a second or so on some of their moves, this means they have a bad connection and the system is compensating for it. You can read more details about how lag forgiveness works here.