Qrxlevmin: defines the minimum RSRP values measured by the UE in a cell to be able to get unrestricted coverage-based service in that cell.
Qrxlevminoffset: Offset of signalled Qrxlevmin taken into account in the Sexlev evaluation as a result of a periodic search for a higher priority PLMN while camped normally in a VPLMN.
Now let me put this in more simple words -
Cell Selection Criteria is Signal Strength/Quality Criteria and described as follows (36.304)
UE would not start registration even though it successfully detected a cell and even decoded MIB and SIBs unless the Srxleve > 0 and Squal > 0. So if a device does not even initiate the PRACH process even when it successfully decoded all the MIB and SIBs, checking on this criteria would be a good first step for the troubleshooting. (Of course, this is not the only issues for this case. there may be USIM issue and Band Indicator Issue, PLMN issues etc).