An assignment patch is a badge or emblem worn as part of one's uniform, to distinguish one's mission or posting. Mission patches were first used by NASA's Gemini 5 crew in 1965, and new patches were created for subsequent missions.
By the 22nd century, with longer-term interstellar missions, these patches came to be identified with a ship, rather than any single mission that ship carried out. Earth Starfleet assignment patches were worn on the left sleeve of the standard duty uniform. (ENTepisode: "Broken Bow", et.al.)
Edit
