Oola is a green-skinned woman of the Twi'lek race wearing little but a fishnet body stocking, a dancer for disgusting Hutt crime lord Jabba. She wears a collar with a leash, which Jabba keeps ahold of at all times.
She's first seen when Artoo and Threepio show Jabba a holographic projection of our hero Luke Skywalker attempting to bargain for the release of smuggler Han Solo (currently cooling his heels - literally - in carbonite). In return, Luke offers Jabba Artoo and Threepio, much to Threepio's horror - an offer Jabba refuses, but apparently decides to keep the droids anyway because he's a jerk.
Apparently refusing deals and getting droids gets Jabba in the mood to party because we cut to a rockin' party going on in Jabba's palace. Oola and another dancer are performing while the Max Rebo Band plays a somewhat sleazy, jazzy tune (in the Special Edition, this is changed to a more upbeat song).
For reasons best known to himself, probably unsavory ones, Jabba gives Oola's leash a jerk, indicating that she come to him as his licks his lips in fiendish delight.
Oola refuses, struggling, and after a prolonged argument in Huttese, her master angrily drops her through a trapdoor, dumping her down into "the pit."
Everyone crowds around a viewing grate and hoots and hollers as we hear roaring and screaming as "something" eats the unfortunate dancer. To drive the point home with a visual metaphor, a satisfied Jabba eats a live frog from his food bowl. We later discover that there's a big door down there and it opens to unleash a ferocious monster known as the Rancor, but that's a surprise for later.
Speaking of the Special Edition, it adds an extra scene actually showing Oola emerging from the chute and landing in the pit, whereupon she picks herself up and watches in horror as the door opens to release the hungry Rancor.
But as in the original the monster's actual appearance is held back until later, and we cut back to the cheering crowd of spectators.