It is possible to apply a glossy varnish to terracotta tiles, so long as the tiles are treated properly beforehand, and so long as you use a varnish meant specifically for terracotta. Terracotta is a hardened clay and porous in nature. This porosity causes it to "drink" in fluids, which can change its appearance and compromise the longevity of the clay.
Before proceeding any further, be sure your tile is clean. It should be swept free of any dirt, dust or grit and gently cleaned of any ground in grime or stains. Do so by using a broom or dry mop, and then washing the tile with an approved tile soap, following carefully the instructions for use. While cleaning the floor, you may perform a splash test to check whether or not the tile has already been treated with a sealer. If the water beads on the tile, it has been previously sealed, and you may not need to impregnate the tile first.
In order to be sure the tile will not drink in your varnish, it must be impregnated. Choose a product that lists itself as a tile protector/sealer, a tile impregnator or both. Multiple coats are painted, rolled or wiped onto the surface of the tile until the substance sits on the surface and no longer soaks into the terracotta. As soon as this happens, immediately wipe away excess and allow the impregnator to dry completely as per the product instructions.
Varnish is sometimes known as a varnishing emulsion. Choose a varnish to add gloss to your tiles that is specifically designed for use on terracotta. Usually reapplied on an annual basis, varnishes do more than add a luminous shine to your floors; they also protect the tile from stains and wear. Apply by wiping the varnish on and wiping up excess, putting on as many coats as is advised by the product you choose.
Maintain the shine and glow of your terracotta by revarnishing yearly, and by washing with an approved polishing shampoo. A quick buff with a wool cloth after washing will bring the floor back to its original luster. High traffic areas may require more in the way of maintenance than quieter areas of your home, as foot traffic dulls the finish.