Generic refers to the members of a whole class of things — like "tissue," a generic word for any soft, thin piece of paper that's good for wiping runny noses.
A generic product, whether it's a tire or donut or drug, is typical of all other products like it. There's nothing distinctive or unique about it. A generic fan looks and acts just like dozens of other fans — it doesn't spin backwards or send out sparks. Generic aspirin doesn't have a trademark, like Bayer or St. Joseph: it's just plain aspirin.