The report shows the maximum allowed cycles for the conditions analyzed and summarized. Of all of those maximum values, one of them is the minimum. This is what is reported as the "Minimum Allowed Cycles".

For example, lets say your model has two elements, and the maximum allowed cycles as computed is:

Element 1: 50,000
Element 2: 48,500

The minimum of these two maximums is 48,500. The report would list 48,500 as the "minimum allowed cycles".