Despite their name, whiteflies are not actually true flies but rather closely related to aphids and mealybugs. Whiteflies are very small (pinhead-ish), winged, and as their name suggests, white in color. They have a very interesting life cycle consisting of four nymphal stages (instars). The first instar (known as a crawler) hatches from eggs that are usually laid on the undersides of leaves. They are so minute that they can rarely be seen with a hand lens. The crawler will, well, crawl until it finds a prime spot to feed. The later instars are immobile and resemble scale insects (reduced legs and antennae, etc.). The winged adult emerges from the last instar and is able to continue feeding.
Damage is hard to spot until you have large populations. Their piercing-sucking mouthparts suck sap causing yellowing or dry leaves but most of the damage is indirect. Like aphids, they excrete a sugary product known as honeydew that can cause leaves to be sticky or covered in sooty mold. However, the largest concern with whiteflies is their transmission of disease to plants.
Depending on the local climate, they can breed year round.
All continents excluding Antarctica
Most species of whiteflies have a wide range of hostplants. Unfortunately, many species love tomato plants and seek them out.
Heavy infestations of whiteflies are difficult to remedy. At the start of an infestation, remove as many infected leaves as you can and heavily spray the undersides of the remaining leaves to knock off any remaining insects. There are also many biological controls such as parasitic wasps available for controlling them. Of course, there are pesticides available but these should be carefully used as a last resort.
What can I say? Whiteflies probably serve a very important ecological role, but can be incredibly damaging to any crop. Remember, everything can be bad in excess but if you start spraying general pesticides indiscriminately you will likely have larger problems in the future with a lack of beneficials.