The Strogg are a malevolent alien race originating from the planet Stroggos. In the Quake games that they appear in (II, 4, and Enemy Territory: Quake Wars), they are battling the human race for the control of Earth and its resources.
The Strogg are typically never seen without some sort of cybernetic implants or attachments; some Strogg, like the Makron in Quake II, take their enhancement to the extreme, leaving nothing but their brain as the last remaining organic vestiges. Strogg not only modify themselves, but they take captured enemies and "Stroggify" them, converting them to hive-mind soldiers of the Strogg. Matthew Kane, the protagonist of Quake 4, is captured and Stroggified, showing it to be a horrifying process where the subject is kept barely alive while limbs are sawn off and mutilated to make way for Strogg enhancements.
The Strogg live on stroylent, a substance created from biological matter, typically the otherwise useless bodies of fallen or weak enemies. In Quake II, the player works through a Strogg stroylent factory, with now-insane human marines and assorted limbs are pulped.
In Quake II it is believed that destroying the Makron, the Strogg leader, will cause enough disarray among the Strogg to make them a non-threat. It is discovered in Quake 4 that the Strogg have created a new Makron and that the Strogg Nexus is a much more important target.