Actually, most gargoyles are not depicted in said manner. Firstly, all true gargoyles have the function of being a water spout, i.e., diverting rain or melt water away from the structure through its mouth. If the creature does not do so, then it's properly called a grotesque.
The history of gargoyles and grotesques is long and complex, probably dating as far back as ancient Egypt. Suffice it to say, for purposes of this discussion, the creatures really began useage in the middle ages in Europe... say the 1200's. As such, their obvious religious symbology came to the forefront. When used on the magnificent stone churches they served the purpose of depicting, to a largely illiterate populace, the reality of evil spirits. The uglier they could be made, the more real the evil spirit could become. Since, at that time, all churches were Roman Catholic, the paritioner could easily see that, outside of the church sat the evil spirits, ready to do their havoc, whereas once the faithful entered the church they saw beautiful statuary depicting the Virgin and saints, as well as the peace encountere, so the message was the safety available within the church, especially from the evil ones..
So, long winded way of saying the gargoyle (derived from the Latin via the Old French gargouille or throat, reffering to the spouting of water) served a useful purpose, but also a symbolic purpose...
One final comment, the most common Gargoyle is the Green Man... the origins of which are really unknown, but quite ancient... but that's another question...