This is a "penny-farthing" bike. You mount it by putting a foot on the step above the back wheel, you push off, then climb up it towards the pedals as it moves away. (Like this video shows.)
The front wheel was so large for a couple of reasons: Since the pedals were connected directly to the wheel, the bike could go faster if the wheel were larger; and also, a large wheel functioned as suspension.
When the safety bicycle was introduced, it had pneumatic tires and drivetrains that allowed for gearing independent of wheel size, so the penny-farthing fell into disuse.