In basketball, minutes can refer to either the minutes left on a period or game, or to the time a player has been on the court during a game. In both cases the word is used to count time, but the situations in which they are applied differ and require an individual understanding.
Game minutes are as straightforward as they sound, it is simply the time in a game. In a television broadcast you may hear phrases such as "There are 4 minutes remaining in this period". That means that there are 4 minutes until the period ends. In the NBA each game is 48 minutes long, while in other places like FIBA basketball and college basketball it is only 40 minutes long.
Player minutes is the amount of time a player has played. A player can play a total of 48 minutes per game in the NBA and 40 in other leagues, excluding overtime. Starters are the ones who tend to play the most minutes, while bench players play less minutes. You may hear phrases like "Paul Milssap's minutes are restricted today". That means the player's playing time is below his usual, probably because he is coming back from injury or simply needs a rest.
Just like there are player per game statistics, player per minute statistics are calculated, although they are less popular and are used most commonly for advanced analysis of the game. A player's "minutes per game" stat is also calculated and widely used, as it is a way to analyze how much he or she has been playing.
Check out a list of the players who played the most minutes throughout their careers in the NBA.