A whale tail is what shows when a persons low rider jeans are riding Really Low, and their thong underpants are simultaneously riding high. What shows then is a portion of the 'waist' band and the top-most portion of the piece that goes from the front waist band, through the crotch, and up the back to the waist band. The two pieces of clothing do NOT work together very well, and the back of the pants are pulled down by the fabric of the legs pulling down when the person sits. Since there is no leg fabric on the thong underwear, the thong sits where it was. They can also ride up higher than they started when the wearer repeatedly sits and rises, sits and rises, and the thong works its way up the inside of the jeans, finally 'surfacing' and staying there until great garment adjustment is done. Because the waist band is wider than the crotch piece, and tapered, and frequently sparkly and decorated in some way, and the piece coming up from below is very narrow, it does somewhat have an appearance or shape of a whale tail breaking the surface of the ocean. Hence the name. It's not meant to imply fatness at all, that I've ever heard, it's JUST the appearance of the thong above the edge of the jeans.
When my girls were in Jr and Sr high, many of their classmates 'let' their underwear (only the thongs) ride up to show that they too were cool enough to wear thong underwear, as opposed to bikini underpants, or heaven forbid, granny panties! They were STYLIN', guys, just too fab for WORDS... Or, so they thought. Now that MY girls are all in their 20's, while they all wear the thongs, they all work at NOT letting them show above their pants, and they think that letting them show, or making them show - looks cheap, and unladylike. Thong underwear, as far as I've been told, derived from the G-strings that strippers wore, so they have, among some people, a taint of that profession about them.