Definitions for "Fan service"
The term originally referred to scenes which were gloriously animated just for fan appeal. It has come to refer to scenes with scantily (or not at all) dressed characters.
In general, fan service refers to scenes designed to excite or titillate the viewer. This can include scantily-clad outfits, cleavage shots, panty shots, nude scenes (shower scenes especially), etc. Some broader definitions also include things like cool mecha, big explosions, battle scenes, etc. Basically, if it has little plot-redeaming value, but makes the viewer sit up and take notice, it's probably fan service in one form or another.
Ecchi, Hentai - These are different terms for varying degrees of sexual content. Fan Service usually refers to non-explicit titillation (i.e. panty shots, jiggle, skimpy bathing suits). Ecchi is more explicit and pretty much implies nudity. Hentai is actual porn. Ecchi dialogue is off-color without outright using explicitly crude words. The words "ecchi" and "hentai" are also used to refer to mild or big-league perverts respectively. ("Ecchi" is the Japanized pronunciation of the letter "H", which is the first letter in the Romaji spelling of "Hentai".)
Keywords:  japan, simply, sometimes, referred
It is also sometimes referred to in Japan as a or simply .