A smoothy is a man who has had all external genitalia (testicles, scrotum, and penis) removed (a penectomized Eunuch). He may also have had his nipples removed.
This term may be considered culturally-specific to men from the "West." Biological men from various other cultural groups may undergo similar procedures (e.g. the Hijras of India), but would likely not be termed a smoothy given the different sociocultural contexts.