Also known as a mesh strainer or skimmer, a spider is a kitchen utensil used to easily douse and retrieve foods from hot liquid, especially oil. Available in good cookware shops and in Chinatown, a spider has a large shallow basket at one end made of open mesh and a long handle extending at an angle of perhaps 120° from the basket. The basket is made of stainless steel or brass webbing (hence the name?); the handle is generally made of bamboo or metal.
When do you use a spider? Let's say you're deep frying a batch of delicious fish cakes. They're a lovely golden brown, and you need to retrieve them from the hot oil. A slotted spoon makes this a labourious task, as you are forced to fish out one cake at a time, leaving the rest to get progressively browner. A spider scoops them all up at once. Or let's say you want to cook some fresh egg noodles in a boiling broth, or blanch a bunch of asparagus. Put said item in the spider, lower it into the boiling liquid, keep it there for about 30 seconds, and pull it out. Very handy.