The boot is what connects the rider to his bindings. The boot provides stability and control over the board. Snowboard boots today are fairly stiff. They are higly technological; featuring many high tech materials which provide high amounts of insulation with little weight.
There are various types of boots today; park boots (for the board park) and racing boots. Park boots feature lace up systems with various forms of keeping your feet dry while combating cold toes. Racing boots are similar to skiing boots; they are made from high strength plastics and are very ridged and stable.
This illustration is a great demonstration of what most snowboarding boots look like.