Well, they both mean 'live', but 'live' is such an annoyingly polysemic (that is, it has multiple meanings) word that it's better to render the translations with different words.
'Abitare' is mainly in the sense of 'reside' or 'dwell'. "Abito in un appartamento" translates to "I live (reside) in an apartment."
'Vivere' also has the connotation of 'reside', but it can also mean 'to be alive', 'to subsist', 'to go through life', etc. "Vivo in un appartmento" means the same as "abito in un appartamento", but 'vivo' can also be used as so: "vivo di carne" - "I feed on meat."
P.S. Both 'abito' and 'vivo' are nouns/adjectives, and they have a lot of meanings in their own respect. The dictionary can explain far better than I can: