The term maximal matching refers to a type of searching and reporting used by regular expression search routines.  When maximal matching is performed, the longest matching string for a given regular expression will be reported as the matched string for a given line.  In the lines below, the bold sections show the minimal match and the maximal match when the regular expression  o.*m is applied to the sample text:

The quick brown fox jumped over the lazy programmer.

The quick brown fox jumped over the lazy programmer.