According to the National Rifle Association National Firearms Museums, the first Winchester rifle was the Winchester Model 1866; it was heavily based on the Henry rifle. The Henry rifle was a .44 rimfire rifle with a 16-shot tubular magazine invented by B. Tyler Henry in 1860.
Wikipedia points out that Oliver Winchester, owner of the Winchester Repeating Arms Company, modified the Henry rifle by improving the magazine and adding a wooden forearm. The Winchester rifle was prized for its lever-action mechanism which made it possible for a shooter to shoot several rounds before having to reload. Subsequent improvements in the Winchester rifle added a loading gate and a round, sealed magazine.