Competitors per Judge is the total number of Competitors that a Judge will be assigned (asked to evaluate) when they check in. Assignments are made automatically when Judges check in, unless you've manually pre-assigned Competitors to a Judge. If you manually pre-assign Competitors to a Judge, their assignments won't change on check-in.
If a Judge has a Tag, he/she will be preferentially assigned Competitors with that Tag.
Please note: This is affected by Wildcards. Wildcards are the number of Competitors assigned to a Judge regardless of Tags. This is useful when there aren't enough Judges for one or more Tags.
If you want to restrict judge matching so that judges do not get assigned any projects outside of their Tags, Wildcards must be set to -1 (negative one).