What do phobos and deimos mean?
Fear and terror.
Phobos gives us the (many) ‘phobia’ suffixes (hydrophobia etc.) and Deimos I think is the same etymological root as demon.
The planets are named after Roman Gods. In particular Mars was the god of war and his Greek equivalent was Ares. Venus was the goddess of love with Greek equivalent Aphrodite. When Mars' two moons were discovered they were named Phobos and Deimos after the twin sons of Ares and Aphrodite.
It is thought that Phobos and Deimos are both captured asteroids. Phobos is orbiting close to Mars and it is thought that in about 50 million years it will either crash into Mars or break up to form a ring around Mars.