A blender is a kitchen appliance which consists of a plastic or glass container that fits onto a motorized base; the container has short rotating blades at its base to chop, blend, puree and liquefy foods. Blenders are excellent for combining cooked vegetables and broth into a smooth pureed soup, or for combining ice, fruit, juice, and yogurt into a smoothie. Homemade mayonnaise preparation is a breeze with a blender, and did I hear someone say margarita? You betcha.
Probably the blender's closest competitor is the food processor, but the two do not work in exactly the same way. A food processor has a flat working bowl that tends to throw food up onto the sides. A blender, on the other hand, has a tall narrow working bowl, so it forms a vortex when blending that sucks food back onto the blades; for this reason, food which contains a fair amount of liquid will be more quickly pureed in a blender than a food processor. However, blenders do require a fair amount of liquid to function in this way, so making a big batch of pesto, say, will work better in a food processor than a blender. In a blender you'll either have to work in small batches, or add more olive oil than is strictly necessary, just to get the blender to function properly. Similarly, blenders make quick work of chopping small amounts of food like bread crumbs and herbs, but large amounts will have to be processed in batches. Food processors can do things blenders can't, like slice and grate, but blenders are much cheaper.
A recent invention is the immersion blender (fuzzy and blue calls it a blender on a stick), a hand-held wand that is immersed in the food to be blended. This is useful for pureeing a soup right in the pot, and ol' fuzzy says for lots of other stuff too, but I still think the old-fashioned counter-top blender is the more versatile.
Professor Pi niftily lists a dazzling array of settings which most modern blenders come equipped with; older ones just had "on" and "off". This vast range of settings are mostly just smoke and mirrors, for the differences between them are miniscule, and really you could make do with two or three. Note too that a glass working bowl will last longer than a plastic one because it doesn't scratch; in addition, it's easier to clean, making it more hygienic.