Cobweb is a term used for messy spider webs in homes, the flimsy webs that sort of drape down and get covered in dust. There is a group of spiders we call the cobweb spiders, but many species of spiders make messy webs we would call cobwebs.
In Iowa the most common species of spider that makes cobweb-like webs is the long-bodied cellar spider. Long-bodied cellar spiders have a long body that is usually a bit less than 1/3 of an inch, and very long thin legs that can make the spider seem quite large. The spiders are grayish in color. Sometimes long-bodied cellar spiders are seen hanging in their web, but most often just the webs are seen because the cobwebs do not become obvious until they are old and abandoned by the spider and have gotten covered in dust. Long-bodied cellar spiders leave what seem to me to be permanent webs in basements, corners of ceilings, walls, book shelves, basically just about anywhere.
Long-bodied cellar spiders are not poisonous to humans and are actually sort of good guys because they eat insect pests, house centipedes, and other things we do not like in our homes. Long-bodied cellar spiders are difficult to eliminate from a home. Often the spiders and webs are concentrated in a dark, seldom disturbed, basement or cellar area. Insecticides are not very effective at controlling these spiders for a few reasons; 1) the spiders don't move around that much so the chances of them walking through a residual insecticide are not good; 2) even if they do walk through the insecticide they are walking on the tips of legs on claw-like tarsi, and 3) insecticides are often not as effective as we want because spiders are not insects, they are arachnids.
For cellar spider control the best thing is a vacuum with a hose attachment. Systematically move through your house, removing all webs and spiders. Repeat this every few weeks until no new webs are seen.