người hâm mộ service, I believe that it is when the những người hâm mộ get to see a little something from the characters (Example: When anime guys are shirtless).
HOTD has a crap ton of it; it's basically an unnecessary pantie, breast, junk, hoặc booty shot. For instance in HOTD these helicopters flew past and (for no legit reason) blew Rei's váy up.
Here's a less explicit example; this scene actually is not what it looks like--he's actually trying to protect her but (as typical fanservice goes) they ended up in this awkward position.