Spinning uses a special bike where you vary the tension using a knob. This gives the illusion of riding up steeper and steeper hills. You don't use your arms, but you can lean forward in a racing position, or upward in the seat.
In a spin class, many people are on bicycles facing the instructor, also on a bicycle, who leads you through a workout, where you pedal and different speeds, using different tensions on the knob (1 through 10), different positions. It is usually very very tough cardio and really builds your legs.
I have a bicycle like yours, probably a Schwinn Airdyne, right? I sort of fake a spin workout by peddling much faster and slower, leaning forward, standing in the peddles and what-not. But it is better with the spinning bicycle, I just don't have access to a gym anymore.