This is a less extreme version of ant-eater cock.
This term is mainly used in a serious situations where you must leave a party or event because you're about to soil your pants and embarrass yourself and others around you.
It's a more discrete way of saying that you need to crap rather than saying it out loud. You simply look at the driver and say, baby dolphin!
We were on a double date last night with the guys and Sarah sent me a text under the table that said 'Baby Dolphin', so I went with her to the restroom so her diarrhea wasn't so obvious.