Tall boots are the formal version of paddock boots and half chaps. The tall boot top covers your leg and does several things: Provides protection from the stirrup leather and bottom edge of the saddle flap, provides grip to the calf, supports the ankle. I spend all day in boots or in half chaps and find that it also helps support the muscles of my lower leg which canfatigue after working ten horses and teaching. There are two designs to tall boots- dress boots and field boots (these have the laces at the front of the ankle). Traditionally field boots were for hunters and cross country style jumping and are considered less formal than the dress boots. The laces allow for room in the ankle of the boot to get the foot in but also allow the rider to lace them for desired tightness to support the flexed ankle in jump and gallop position. True dressage dress boots are actually much stiffer through the leg and ankle to support the stillness of the leg (and less ankle flexion) required for upper level movements.
If you are interested in feel of them start with an inexpensive pair of half chaps fitted around your calf snug. Personally I don't ride without either my tall boots or my fitted half chaps.