Many people are drawn to the idea of a single lens that covers every need from 18mm wideangle to 200mm telephoto and beyond. Such an optic would avoid the need to ever change the lens, so you'd never miss that once-in-a-lifetime shot because you had the wrong one fitted, and of course you'd never get dust on your sensor.
If you suspect there must be a catch then you're right, there are trade-offs with such lenses. In general, the longer the range, the more the optical quality tends to suffer, with lower contrast, poorer edge sharpness and greater distortion. Superzooms are jacks of all trades but masters of none, and will be outperformed by prime lenses, and many zooms with a shorter range.
The maximum apertures are pretty small too (as low as f/6.3 at the tele end) so you may have to raise the ISO more often to shoot handheld.
However, depending on what you photograph and the level of quality that you demand, you may find these to be sacrifices worth making. The fact is that at smaller print sizes the average user is unlikely to spot many of these optical deficiencies, so they are fine for users who want reasonably good pictures that won't be printed too big or studied with a magnifying glass.
Superzooms are physically a bit larger than lenses with a shorter range, but not as much as you may expect. In fact modern superzooms are miracles of optical design, being smaller, lighter and offering better quality that could have been dreamed of a couple of decades ago.
Superzooms offer the most extreme zoom ranges available covering every popular focal length from the widest end of the typical kit lens to the longest end of the average telezoom.
The wideangle end is ideal for general scenic views and group shots, while the telephoto end is perfect for zooming in to sports, wildlife, candid street scenes and any situation where you want to shoot from a distance.
Lens Top Tip
Make sure you get a superzoom with built-in Image Stabilisation, unless you have an Anti-Shake sensor built into your DSLR.