Whatever the setting, these games all have four primary goals.
eXplore refers to the fact that the player starts out with limited knowledge of the playing area or map. This can be reflected either by large areas of the map that are completely blank or obscured (such as with a fog of war), or some features may be visible with limited information (for example, the stars in Master of Orion).
eXpand refers to the need for the player to expand the territory under their control. This can be done by creating new settlements, or expanding the areas under control of existing settlements.
eXploit refers to the ability of the player's empire to use the resources within their territory, and to improve the efficiency of that usage.
eXterminate refers to the primary victory condition for this type of game: eliminate all rival civilizations. The earliest 4X strategy video games had this as the only victory condition, but in an effort to be more realistic, many games in the genre now have other victory conditions. A good example of this is in the Sid Meier's Civilization series, where the first two releases could be won by either conquering the world or by constructing a spaceship, and launching it toward Alpha Centauri; Sid Meier's Civilization III on the other hand has six different victory conditions.