Vivere has a more general meaning ("to spend one's life"), while abitare stands for "to reside somewhere, to live in a concrete place". You can, for example, say "Io vivo dai miei genitori" as well as "Io abito dai miei genitori", but you can only use "vivere" in sentences like "io vivo felice" or "lasciami vivere in pace!".
This is how I think of them: The English equivalent for vivere is "to live" which is used not only for where but also how we live. It has greater scope than but can also be used like abitare which is 'to inhabit or 'to live in'. Abitare is about where we live , that which we live in, our habitation or habitats. I think this fits with d.batta's examples in Italian. "I live with my parents".and ALSO "I live happily" and "Leave me to live (my life) in peace" Whereas the abitare equivalent is "I inhabit the house of my parents'. or in my case "Abito in montagna perché voglio vivere così"