Essentially applies to series (of any franchise) which frequently add characters to an already massive pool of characters (although not necessarily negatively). However, In a more negative-context, sometimes this term may refer to the observation of a series feeling "over-crowded" with characters.
The term is along the lines of various other enumerated "rules" of internet (such as rule 34 and godwin's law.
Rule 151 comes from the Pokemon franchise, as there is constant expansion of the number of various 'monsters' in the games/series.
As said before, this can be applied to anything, not just the Pokemon franchise, but also to other things which seem to demonstrate a similar tendencies.
"Rule 151. As long as the series runs, there are always more characters to add"
"The new Pokemon games just came out. But I'm not sure how many more monsters they can come up with"
"Well, Rule 151"