(written from a Production point of view)
A background character is a character that rarely has speaking lines, but often appears in many Star Trek episodes.
The best known Star Trek background character is Star Trek: Deep Space Nine's Morn (Mark Allen Shepherd), who appeared in more than one hundred episodes of the series. As well as even being frequently mentioned, he even had an episode based around him, "Who Mourns for Morn?". Other background characters in Deep Space Nine include Broik (David B. Levinson), M'Pella (Cathy DeBuono) and Lieutenant Jones (Randy James).