This game mechanic is fairly straightforward and is used in most games. The player receives a level which determines the strength of their character, the items they have/can use, and the abilities that they have. It is used across a wide range of genres as it can affect the player in a different way.
The first example where this mechanic is used is in Counter-Strike: Global Offensive. The player has two levels which each serve a different purpose. The first is a level that starts at 1 and ends at 40. The purpose of this is to give player rewards when they reach certain levels and works using the progression mechanic. The good thing about this is that it means that the players have to reach level 3 before they can play the competitive side of the game. This is where the other form of level mechanic is used. In the competitive game mode, the player has a rank which determines the skill level of them and the players they will be matched up with. This is done so that the games are fairer and the players have an equal chance of winning.
Another game that uses this mechanic is Lord Of The Rings: Online. This is an MMORPG where the players aim is to reach the highest level. The mechanic is used in this game so that as they level up the strength of the character increases and they can defeat higher level enemies. It also means that they can explore different areas of the game that require a certain level.
If I were to use this mechanic in a game it would be tied in with the reward system. The player levels up by the progression mechanic which then gives them points to spend on abilities. This would be effective in open world resource collecting games similar to Minecraft.