After her mother was struck with a beam of radiation containing the DNA of several different types of spiders while she was in-utero, Jessica Drew developed superhuman powers patterned after several different types of spiders when she was born.
In addition to her powers, she is also a superb hand-to-hand combat fighter, and has trained in several styles of fighting including boxing, judo, karate, and capoeira, learned under the training of the Taskmaster.