This is a word made from two words; Taylor and Orgasim.
Taylor is from the singer Taylor Swift and Oragsim is self explanatory.
The term Taylorgasim is an orgasim you get which has anything to do Taylor Swift.
"I just watched Taylor on youtube and so had a Taylorgasim"
"OMJ! I just got tickets to see Taylor Swift live, its so TAYLORGASMIC"