A repeater used in cellular systems does exactly what the name suggests – on the downlink, it receives the signal coming from a base station, amplifies it and retransmits (usually in a direction facing away from the base station).
On the uplink, the process is exactly the same. There is no demodulation of the RF at the repeater – it is simply a two way RF amplifier.
Their function is to extend the areas of coverage of a basestation – particularly in areas of low traffic.