There are levels or stages to game testing. At the most basic, a game tester is going to be responsible for playing a game while it is in development and reporting bugs (problems that need to be fixed). At more advanced stages of testing, you will be responsible for addressing the game for what it is: software. This means you will have knowledge of how software works and will approach testing a game in a methodical way, addressing areas of high risk and complexity with a strategic approach to find bugs faster, or find deeper issues instead of cursory issues. As experience progresses it is natural to become profficient in computer languages such as C++ and scripting languages such as LUA to be a SDET: Software Developer in Test, where you will write your own code to exercise the game you are testing in an automated fashion.
To continue on with what Korey said, there is testing to make sure the software is working properly and there is testing to make sure the game is entertaining. Much of the detailed testing is done by full-time employees or even contracted out to service providers who follow detailed test plans and which involves lots of repetitive actions. You might test a quest boss fight by trying it with each character type, with each weapon, with each spell, etc. You might spend the day making each character jump out of a window to make sure they all react properly.
But you can also be the type of tester that checks the flow and entertainment value of the game. Is the difficulty progression smooth and logical? Are all of the characters playable? Is there a class so out of balance that no one wants to play it? Sometimes this is tested by bringing outsiders into the studio to playtest a new mission or level. Sometimes a "public beta" is run where people play the game from home under more realistic conditions. Technology allows for a lot of variety here.
Game testing means dig deep inside the game to experience user interface, errors and bugs done through programming and the core of game mechanics like movement or aim in FPS games.