We learn a lot more about the malevolent yin to Harry's righteous yang in later chapters of the saga, but for now, it's enough to know the basics: he's evil, he's scary, and he tried to take over the world about eleven years ago.
Harry Potter stopped him, though how or why not even he knows, and Ol' Vol's just itching to get back at the little guy.
That's sufficient to get our heroes scuttling after the Sorcerer's Stone before he can get to it, making him more of a dramatic impetus than a character. Indeed, all of the traits we do know about him—for now at least—come second- or third-hand, and don't seem to do more than confirm his basic evilness.
The movie doesn't need any more than that, and frankly with seven more on the way, it needed to save its powder as far as Voldemort's personality goes.
But there's something else that defines Voldemort, beyond his whole here comes a scary bad guy thing: his connection to Harry. It's clear he's had a huge impact on the course of Harry's life, what with killing of his parents and all.
But Harry's also put a serious crimp in Voldemort's style, and with that scar in place, we never forget just who's waiting at the end of Harry's road. That may be what leads Voldemort to tempt Harry into joining him instead of just killing him:
VOLDEMORT: Tell me, Harry, would you like to see your mother and father again? Together, we can bring them back.
It's a tempting offer…and it's also a super low blow. Harry knows that Voldemort offed his mum and dad, so the fact that Voldemort is saying he can bring them back is a bit like saying "Hey, I stole your laptop. If you become friends with me, I'll give it back."
This exchange also does something else—it shows how important Voldemort knows Harry is. It's not every day that an immensely powerful wizard tries to join forces with an eleven-year-old kid. Harry knows that, this time and every time, it's personal.
From that moment, the rumble is on. The Sorcerer's Stone is just the opening skirmish in a very long war, and, as the later books tell us, "neither can live while the other survives."