The term time has a number of different meanings in poker, but the most common is when a player asks for extra time to make a decision:
To ask for extra time to make a decision[]
A player may ask for time (by merely stating "Time!" or "Time, please!" out loud) if they will require more than the usual amount of time when it is their turn to make their decision about which betting action they will take.
Generally, players are allowed only a few seconds (3-5 seconds, as a rule of thumb, though taking up to 10 seconds is usually allowed without even a comment) to make a decision when it is their turn to act. Players who need more time should always ask for "time" out loud, since other players or perhaps even the dealer may not notice the delay and may assume the player has already acted and folded, and then act themselves, thinking they are acting in turn. If enough players do this, the player who delayed may end up being forced to accept having "already checked", depending on the rules of the cardroom, though in "friendlier" games the delaying player may be allowed to act late, depending on the situation and their intended action.
A player who asks for "time" is usually granted virtually unlimited time to make their decision, but most cardrooms have provisions to handle cases where players take an inordinate amount of time. Usually this requires another player at the table to "call a clock" on the offending player, at which point a sixty-second timer is started. If the delaying player has not made their betting action by the time that sixty-second timer runs out, their hand is checked or folded, as appropriate. From a purely practical standpoint, this doesn't really happen in physical casinos much; players are in general courteous and respectful of the time of others and make their decisions in a timely manner. If they can't make them in 3-5 seconds, they will generally ask for time and then make them within about 15 seconds or so.
In online play, players are allowed only a fixed amount of time in which to make a decision (usually 10-15 seconds), after which their hand will be automatically checked, if possible, or folded if it cannot be checked. In some cases, online casinos give players a time bank of extra seconds they can use to think about a decision, ranging anywhere from 10-90 extra seconds of time. This simulates asking for "time" out loud in a physical brick-and-mortar casino.
To chastise players who act out of turn[]
Dealers will often call "time!" to the players on a table if the action skips a player on a betting round for no apparent reason. Sometimes this is because a player in middle position acts out of turn and the player after them sees the out-of-order action and assumes it's their turn, etc. Other times, it's honest confusion from players who aren't paying particularly close attention to the game and accidentally skip a player. Dealers will essentially ask for time for the player without the player having initiated the action (usually because the player is unaware that action has skipped them).
If the players are being noisy, or having side discussions and not paying attention to the game, the dealer will often use a shout of "time!" to get the offending players' attention and let them know they aren't paying attention and have just acted out of turn.
To prod a player into action[]
Dealers may declare "time", or "time, please" if they encounter a player who is taking what seems to them to be a long time to make an action. This is essentially the dealer doing what they would want the player to do in this situation, but I've seen dealers use the phrase to prod players into action even after only a second or two. In this case, the dealer is basically saying "hurry up" to the player.
To pay a house fee based on time played rather than a per-hand fee[]
There are two standard ways for a casino to calculate the fees it charges poker players: one is a per-hand rake, where the casino takes a piece of every pot that is played. The other is a time charge, also called "paying time".
A time charge is where the house charges each player seated at a poker table a fixed fee at some sort of regular interval. Usually, this interval is a half-hour. The house then does not take any money out of the pots won at the table.