TURN stands for Traversal Using Relays around NAT. Like STUN, it is a network protocol/packet format (IETF RFC 5766) used to assist in the discovery of paths between peers on the Internet. It differs from STUN in that it uses a public intermediary relay to relay packets between peers. Messenger uses TURN to exchange media stream packets when no other option is available since it consumes server resources and has an increased latency due to the extra step.
The only time when TURN is necessary is when one of the peers is behind a symmetric NAT and the other peer is behind either a symmetric NAT or port-restricted NAT. The frequency of cases where a relay is necessary is difficult to pin down, but is estimated to be around 8% (source)