An assimilation chamber was a section on a Borg vessel where the assimilation of an individual or group of individuals into the Borg Collective was performed. (VOY: "Dark Frontier")
Assimilated individuals were brought to these chambers after being injected with nanoprobes to be fitted with their permanent implants and exo-plating. Here, individuals underwent forceful and invasive surgical procedures to remove limbs, and other body parts in preparation for receiving these implants, often while fully conscious.
Once complete, a new drone is formed. (Star Trek: First Contact; VOY: "Collective", "Dark Frontier")