What is LOOP BACK MODE?
It means that everything you send out comes back as input, without making it to the underlying bus (for example: UART, SPI etc.). Have you googled it?
As Tamir says, it generically means that the output is "looped" back to the input:
Output-------->+ | | Loop-back | Input<---------+
Clearly, if you now receive at the input what you (thought you) transmitted from the output, you have demonstrated that the output, the loop-back connection, and the input are all working. This is, obviously, a very useful test!
For specific details of precisely what is looped back, and the point at which the "loop" is connected, you would have to consult the documentation for the specific system in question.
Often, there are various different loop-back modes to allow testing of various different parts of the system...