It wouldn't be Spider-Man without a little genetic mutation; after all, Peter Parker himself was bitten by a mutated spider, which gave him super powers. In the movie franchise, other people - including Harry Osborn - covet Spider-Man's blood for its potentially healing properties.
Oscorp Industries, the fictional company that's the root of evil in this Spider-Man story, is a genetics laboratory where scientists work on experimental, cutting-edge research. Scientists at Oscorp have tried to combine human DNA with other animals in order to genetically engineer super hybrids.
While animal-human hybrids are largely considered the stuff of legend, real-life scientists have grown cartilage in the shape of a human ear on the back of a mouse. And other animals, like a lion and tiger, can interbreed, creating hybrids.
Max Dillon (played by Jamie Foxx in the new movie) worked at Oscorp until an accident at the plant turned him into the villain Electro. After the accident, Dillon mutated, becoming a powerful villain with electricity instead of blood running through his veins.