Terminologies used

The Test department of a game publishing company is called "Quality Assurance," or "QA" for short. The term "QA" is also often used to describe the function or process of testing. In this article, the terms "test" and "QA" are sometimes used interchangeably.

Also note: This article is discussing the full-time internal job of tester (wherein the tester is an employee who comes to work daily at the game company to test games, for wages). Volunteer (unpaid) "beta testing" (wherein someone at home gets a copy of a game and provides feedback via email, usually without pay) is a separate matter entirely. Getting a job as a tester can be a good way to get started in the game biz -- volunteering to do some beta testing is more akin to simply being a customer (an end user).
Quality Assurance testing jobs are usually found at game publishing companies. Developers also do some testing (but usually not full Q.A.) - but game development companies probably don't have full-time testing jobs (unless the development company is very large and well-staffed).

Typically, someone who works at a small game development company usually performs multiple job functions. Publisher jobs are usually more specialized. So someone who starts as a tester at a publishing company might eventually move up into producing, while someone who works as a tester at a smaller development company might eventually move up into any of a number of roles.

There are also independent testing labs who hire testers. Publishers are increasingly outsourcing their Q.A. to these outside labs. Jobs at these places are okay if you just want to test and you don't have aspirations of moving up in the industry - a tester who works at one of these labs would have to quit in order to move up in the industry. It's recommended that if you want to work as a tester as a steppingstone to other jobs in the industry, that you work for a publisher or a large developer, not an independent test lab.