This game built on the revolutionary beginnings of one of the most influential RPGs of all-time: Phantasy Star for the Sega Master System. While it encorporated several aspects that made the original so great (expansive universe spanning 3 planets, compelling story, great fighting, the best graphics of the day), it also added some innovations.
First, while you would meet friends who would join your party, you had to mix and match the players based on their specific strengths. The categories were familiar, gun-specialist, doctor, mech specialist. However, some were unique: Amy is a clepto who will steal useful items at certain points of the game, if used correctly.
Also, long before it happened in FF7, Phantasy Star II killed off a main character. At the time, it was shocking. I remember reseting the game and trying again because I couldn't believe a main character could die. This storytelling innovation is now much used, a tribute to the success of Phantasy Star II.
The graphics, music, and challenges were all great, and the game retains much of the replayability to this day. However, it could be too challenging: the game came with a hint book, without which you could spend countless hours leveling up to try and navigate some huge and complicated dungeons.
In the end, this is one of the best games on the Genesis, and one of the best RPGs of all time.