The underlying concept of Punctuated Equilibria was to take ideas about speciation from current evolutionary theory and work what we should expect to see in the fossil record.
Mayr's ideas about allopathic speciation may be summed up as follows:
A sub-population on the edge of a species' range is cut off.
Without the stabilising effects of gene flow and with differing selective pressures this smaller population diverges quite rapidly, and becomes a new species.
Speciation, then occurs in a relatively small area over a geologically short period of time. Gould proposed that it might only take centuries, perhaps somewhere in the region of 1000 years.
If speciation occurs rapidly in a limited area we will only observe it in the fossil record if we have a very good record for that exact time and place (which is limited by our explorations, as well as by the limits of the record itself). While we have such records for some times and places they are more the exception than the rule.
It follows from this that speciation events - and the fine intergraduations of form that should have existed - should be very rare in the fossil record.
The original 1972 paper may be found
here (scanned text, PDF format)