A memory wipe (a.k.a. mind wipe) is the removal of an individual's memories. It is utilized by the Ghost Program when the shortcomings of the psychic dampener became apparent in the wake of Sarah Kerrigan's defection in 2491. As such, memory wipes became standard operating procedure, allowing for more permanent control of its ghost agents.
The memory assignment protocol is run by an electrical device based in a room which nullifies the use of psychic powers. It is generally operated by Superintendent Sarco Angelini, himself a ghost.
In addition to long-term wipes, a wipe can be used to erase memories from a specific span of time. The device wouldn't be used on a severely injured ghost, however. Some residual memories may reside in the subject after a memory wipe, which can possibly influence their personality on the sub-concious level.
Terrazine can reverse the effects of a memory wipe through its rejuvenation of a telepath's brain cells. In addition, some forms of psychic trauma, such as that inflicted on Gabriel Tosh, also render memory wipes ineffective. In a more practical sense, ghosts can potentially learn of their previous missions by way of stored files, though these files require top-level clearance to access, with said access being doled out on a need to know basis.