For a guy on the 40 man roster, any minor league assignment of less than 20 days will count as major league service time.
So if you were to leave a guy down for the first 15 days of the season and then promote him to the majors, those 15 days would be counted as major league service time (even though he was not in the majors).
But if you leave him down for the first 21 days of the season, and then promote him to the majors, those 21 days would NOT count as ML service time.
For purposes of arbitration and free agency, a ML season is considered to be 175 days (even though a full ML season is more like 186 or so). So the "wait 20 day" thing essentially delays arb and FA by a season.