Please tell me what type of retainer are there and what are they used for?

Retainers: There are several types of both removable and fixed retainers which are used to hold teeth in their position once orthodontic treatment is completed. Removable retainers may be made of metal and plastic or purely plastic while fixed retainers have brackets and/or wires bonded to the teeth.

Retainers: Retainers do one thing, they hold teeth in their current positions if worn as directed. A retainer is different than an appliance that moves teeth. Some are fixed, some removable. Each has advantages and disadvantages, as does any treatment modality. They do similar, but not identical, things. Your question is to broad to answer in this limited space. See a specialist Orthodontist for info.