The Navicomp is a type of computer 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.
Since Red Dwarf was a massive ship and could be controlled from a number of different locations (such as various Drive Rooms and Science Rooms), there are actually a number of navicomps present aboard Red Dwarf.
Dave Lister once had to manually link the navicomp of Red Dwarf to the drive computer in the central Drive Room, 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. ("Future Echoes", Series I).
The navicomp of Starbug 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).