Tea lights are small pillar candles which are molded in a heat-resistant shell. They are so small - perhaps three or four centrimetres in diametre, three centimetres high - that the wax completely liquifies soon after the wick has been lit. The burning candle "feeds" off the molten wax, and most modern wax tea lights will naturally extinguish themselves in about an hour, after all the wax "fuel" has been used up. Votive candles are similar to tea lights but about twice as tall; lacking a heat-resistant shell, votives must be burned in a container into which they will liquify.
Votive candles are used in religious settings, but tea lights are more prosaic in function. Tea lights used to be used to keep pots of tea warm; also to warm pots of potpourri, releasing a lovely scent; and to keep containers of food warm in a buffet-style serving setting. sloebertje tells me she does indeed use a tea light to keep her tea warm; I use a tea cosy or tea cozy, though the general consensus seems to be that they are only for grannies. Ah well; we all know that many of those grandmotherly touches are eminently practical. Tea lights are seldom used these days to keep food warm (we have pots of long-burning oil for that), but they are popular as aromatherapy diffusers and as home accessories. A wide variety of tea light holders is available at trendy home decor stores; I'll leave you to choose the type of holder that pleases you, but I would like to advise you that Ikea sells huge bags of tea light candles at a ridiculously low price.