The Y-DNA STR test determines the number of repeats at a selection of STR markers on the Y-chromosome. STR markers are "short tandem repeats". They are sections of DNA that vary in the number of copies of a simple repeat sequence. STRs tend to change more frequently than other sections of DNA.
You can select to analyze just 20 STR markers, 44 markers or 101 markers. The more markers you test, the more stringent your comparisons will be when matching against another individual. For example, a perfect match with another individual at all 101 markers will be a far stronger match than a match at only 20 markers. If you have a 20 marker match with another individual, comparing more markers will provide further clarification of the relevance of the match and will allow you to see if you continue to match when more markers are compared.