Time reversal is a transformation that inverts the time dimension. It is a discrete symmetry. It operates as
This does not invert the flow of time. It just means that the process is seen from end to beginning instead of beginning to end. The process still happens in normal time. Essentially, it tells us is the Probability of an event remains the same if we look at it in reverse.
The Universe, at least on a macroscopic scale, does not seem to exhibit time reversal symmetry.