Chess games have had time limits for the last 150 years or so. (Before then, games could go on forever.) Each side starts with an equal amount of time. If you don't finish your game before your time runs out, you lose (except for certain situations where your opponent doesn't have enough material to mate you.)
Those time controls you quoted give each side a starting amount of time and add additional time for each move completed.
So 5 2 gives each player 5 minutes and adds 2 seconds for each move completed.
2 1 starts each player with 2 minutes and adds 1 second for each completed move.
15 10 is 15 minutes for the base time with 10 seconds added on for each move.
And so on.
Greetings everyone. I'm kinda new here and also a chess beginner. Some one should please help me explain the chess time stuff, I mean where you select the kind of game time you want. Most especially those like 5|2, 2|1, 15|10 I don't understand these ones at all. Thank you.