A cyclocross bike is similar to both a mountainbike and a road bike.
The wheels are the same size as a road bike, 700c but there is plenty of clearance between the fork and frame so that mud doesn't clog up the wheels too quickly. The tyres have knobbles on them 
so that they can cut through the mud and get grip but not too many so that they can still roll quickly on the tarmac.
so that they can cut through the mud and get grip but not too many so that they can still roll quickly on the tarmac. In a 'cross race you sometimes have to shoulder your bike to get up bankings which are too steep to cycle up.
Like this