Why do you supply both min and max Synopsys .lib files for a particular process corner?

The delay times given in the 'max' library are the longest possible time it can take for the signal to change, from the clock edge. This is used for checking propagation delays & setup times. The delay time given in the 'min' library is the shortest possible time it can take for the signal to change - effectively an output hold time (i.e how long after the clock edge the old value can be considered to be valid). This is used to check for hold time problems.

In the case of some signals, no delay is given, because we do not characterize the output hold time as part of the pre-fab characterization process.