Disc brakes have trickled down from motorcycle and automobiles to bicycles because mountain bikers who were riding in demanding technical conditions found that regular rim brakes weren't working as well as they wanted. With rim brakes, you squeeze your levers and pads rub on the rims to slow and stop you. This works great in dry conditions. But, as the trails get sloppy with water and mud, the pads slip on the rims, weakening braking.
Also, the dirt in the mud wears the pads quickly, in some instances completely, which creates a dangerous no-brakes condition. Sand and muck aren't good for the rims either and over time, the rims can and will wear out forcing an expensive wheel repair. Another brake compromiser is rim damage. If you warp or bend your rim on a ride by hitting a hole or rock, it'll hamper and might even ruin your braking.
So, mountain-bike designers started looking for solutions to these problems and settled on disc brakes, which are common on motorized vehicles. On these brakes, discs are attached to the wheel hubs and calipers are attached to the frame. When you operate the levers, pads inside the calipers squeeze against the discs and stop the bike. Because the discs and pads are designed specifically for braking, they can stop as well, or better than rim brakes and do so in all conditions. What's more, all rim damage associated with braking becomes a non issue. And, rims can be designed differently (and improved) because they no longer are part of the brake system. When you've got discs, should you damage a rim while riding, it has no effect on the brakes.
While it's possible to add disc brake systems to most bicycles, depending on what you need, it can cost quite a bit to upgrade. So, it's best to bring your bike in so we can show you what's needed for your situation and make recommendations. It may make more sense to buy a new bike that comes stock with disc brakes. You'll spend more, but you'll also get all new equipment designed from the factory for disc braking so everything on the machine, from the frame and components to the wheels, will be just right. And, you can even consider selling your used bike to cover the difference.