Rollers require that you balance the same way you have to to ride down the road. The first time most people see a cyclist on rollers in fact, they're often amazed because they can't figure out what's holding the biker up. What's happening is, he's balanced on three spinning drums (the rollers) held in a frame, two that the rear wheel rests on and one (sometimes two) for the front wheel. The front rear drum is attached to the front drum with a belt, so that as you get the bike wheels spinning, all three drums rotate at the same speed. This creates the same gyroscopic effect that helps you balance when you roll down the road outside.
Of course, just like riding outside, if your attention wanders, you'll steer right off the rollers and fall over. You won't go flying through the sliding door and out into the garden though, because there's no forward momentum. Remember, you're not actually moving forward, just spinning in place. As soon as the tires hit the floor, they'll stop and you'll fall over (watch out for that glass coffee table!).
Indoor trainers are very different from rollers. They're stands that the bike is attached to so you can train in place. You don't have to balance at all because the trainer provides a very stable platform that supports you. Both trainers and rollers usually provide resistance devices to create drag.
The significant differences in design between the two devices means that efforts you can do very easily on a regular trainer such as sprinting or spinning rapidly to elevate your heart rate or standing in a big gear (along with staring at a TV screen and watching an inspirational video) -- are difficult to do on rollers, without lots of practice.
Rollers are great for teaching you to ride a straight line and for learning how to relax your upper body. And they make the time pass because you're preoccupied with staying on and remaining smooth. But most indoor bikers are more interested in getting a quality workout than becoming a better bike handler. Trainers are better for this because they support you and take the balance and control out of the exercise equation.
We stock different indoor cycling devices and we're happy to show you what we recommend.