Time Systems limit the period of time available to each player.
Typically there is a device for that purpose, called clock, which at least shows the remaining time for each player and who's turn it is.
Players hit it alternately to signal turn completion, stopping their side of the clock and resuming the other. Depending on the time system, this may trigger further actions. As soon a player exhausts all time[1], the player loses on time (no matter if the turn was complete[2] or not).
Common time systems for Go are
Less common for Go are
See also
[1] Time may also include other things, like number of lifes. For instance, eight hours Japanese Timing in periods of one minute is like having a single one-minute period backed up by 479 lifes.
[2] With no timekeeper, a move is complete when the clock is hit.
[3] Time systems can be combined. T1 plus T2 means that the player who would have lost by time under T1 instead enters T2 and continues. This option is like being backed up by one life.