The Navicomp is a type of computer, found aboard spaceships such as Red Dwarf and Starbug, which controls flight operations. It is presumably a contraction of the words "navigation computer". It can control the ship on autopilot, though this was said previously to be done by Holly in "Backwards". It plays its most major roles in Series VI and Series VII.
Lister once had to link Red Dwarf's navicomp to the drive computer, because it couldn't cope with the influx of data at light speed. A future echo had convinced Lister that this operation would kill him, but later learned that it was his son Bexley who would die whilst operating the navicomp in the Drive Room. (Future Echoes, Series I).
Starbug's navicomp was infected at one point by the Armageddon Virus, which locked out any attempt to access controls and set Starbug on a collision course with a nearby lava moon. (Gunmen of the Apocalypse, Series VI).