In real-time strategy games, an expansion is a secondary base located at a resource node with the express purpose of increasing your resource intake. As with most RTS games, as one's resource intake grows, one can produce more units at once- and thus, will be able to destroy your opponent easier. Most maps will have one or more expansion sites to peruse once you have the spare resources to invest in the creation of such a secondary base.
While expansions are very useful, they are also often vulnerable to attack. These resource nodes are often located in more open territory than the primary bases, and even when terrain such as uncrossable territory or high ground poses a barrier, they do not often possess the space necessary to construct defenses. Thus, while an attack on an opponent's primary base can be a fatal stroke, destroying his expansions can be considered the equivalent of hamstringing him- it is seldom as difficult an attack to complete successfully, and can severely hamper him later on in the game.
In the world of gaming, expansions are extensions to the main product. With a CCG, an expansion entails adding to the available card base, providing for the construction of new deck ideas or the reinforcement and strengthening of old ones; with computer games, the additions range from new maps or areas to new character classes and races. As expansions usually just consist of adding on to current code or reworking things with different methods, they are often far easier to produce, playtest, and market than an entirely different game- and as such, are a company's best bet on milking the cash cow of a popular game as long as they possibly can.