Why raised beds? Many reasons, actually. For one thing, drainage is much better in raised beds. A couple of summers ago we had more rain than usual, and a lot of gardens were waterlogged. All plant roots need to breathe, and if the roots are sitting in water all the time they cannot get any oxygen. It's not a pretty sight.
For another thing, raised beds allow gardening without trampling on the soil near the plant, and no trampling means more oxygen can get to the roots. Packed-down soil is not good for plants. Soil in raised beds warms up earlier in the season, so you can plant earlier. The plants are a little higher so they are easier to work with. You don't have to stoop as much to weed or to water. Fertilizer is easier to apply because you know exactly how big an area you are trying to feed. If pests are a problem, it's usually easier to protect crops in raised beds. If your backyard soil is a problem, you can fill a raised bed with whatever kind of soil you buy. And raised beds bring a certain neatness and organization to your garden.
Here is a view of my raised beds from my bedroom window:
You can make your own raised beds, as I did, or buy a kit from any of several suppliers on the internet or from catalogs. One thing you have to consider when using raised beds is whether or not your wood is treated to resist rot. Treated wood will last much longer, but some gardeners fear that the chemicals used in treating the wood might leech into the soil and in turn into the plants you eat.