fan service put simply is stuff the producers do to boost rating usually in più mature anime. The most common one is revealing a girl's undergarments in some way o form. Why is this bad many great manga get turned into animes with to much fan service. fan service often can ruin an Anime and reduce its amount of viewers. Not to mention it also lowers the chance of it ever becoming dubbed.
I will now give examples of some animes that overdid this compared to its manga.
1 rosario vampire in the manga it is teen at most parts at least, In the Anime they put a pantie shot almost every 3minutes which can be really annoying and ruin the epicness of the scenes.
However the worst one of my lista is girls bravo. This Anime went beyond words of fan service. The manga was about 15 plus and had few doccia scenes.
In the Anime there was about 3 bath scenes with nudity per episode making it was mature.
HOPE THIS HELPED THOSE WHO DO NOT UNDERSTAND THE TERM fan SERVICE.