In static timing analysis, slack indicates whether timing is met along a timing path.
A positive slack means that the signal can get from the start point to the endpoint of the timing path fast enough for the circuit to operate correctly.
A negative slack means that the data signal is unable to traverse the combinational logic between the start point and the end point of the timing path fast enough to ensure correct circuit operation.
This means your system has some kind of timing violations.
I don't know what means "how it affects timing". If there's negative slack, the timing is kind of failed. The whole system would not be working.