The purpose of TTI Bundling is to improve cell edge coverage and in-house reception for voice.
When the base station detects that the mobile can't increase it's transmission power and reception is getting worse it can instruct the device to activate TTI bundling and send the same packet but with different error detection and correction bits in 2, 3 or even 4 consecutive transmit time intervals.
The advantage over sending the packet in a single TTI and then detecting that it wasn't received correctly which in turn would lead to one or more retransmissions is that it saves a lot of signaling overhead.
Latency is also reduced as no waiting time is required between the retransmissions. In case the bundle is not received correctly, it is repeated in the same way as an ordinary transmission of a packet.