Fanservice is just what you would think it is, certain enticements to keep viewers interested when you lack certain things like cohesive and interesting story and plot. What this usually entails is female characters with various prominent features.

Anytime you see a female character in a skimpy outfit, flashing her pantsu or letting her cleavage hang out, this is an example of fanservice. For instance, almost every anime has some sort of beach/swimsuit episode.  Even Bleach, a very mainstream anime, has a beach episode.  Seeing your favorite anime girls in bikinis isn't something you see everyday.

One of my favorite fan service animes is Ladies vs Butlers. What little plot there is involves one large breasted girl fighting with another large breasted girl over a guy who usually ends up walking in on at least one girl per episode, who just happens to have her breasts exposed. However, what the story lacks is made up in the presence of the kinky nudity scenes. The specials even push the boundaries of hentai, but I'm not going to go into that...

White clouds, everywhere!  Uncensored version- NSFW- in other words, BOOBS.

Of course, this brings up the topic of boobs in anime. Boobs in anime are like boobs in real life, except that they seem to have a life of their own. But if animators are going to go to the extent of giving them their own physics, making them unrealistically big and jiggly is a given. Most animes don't go as far as showing fully exposed boobs, and when they do, the nipple region is usually hidden by strands of hair, clothing, arms/legs, or random objects flying through the foreground. A lot of animes don't even show anything more than cleavage, just so they keep their viewer base broad. However, some animes are able to show boobs and still stay out of the ecchi category all together.

Now I could write a long essay on why people react strongly to human nudity, but that’s a whole different story. The same goes for porn and hentai, who are usually made for different purposes. While nudity are porn are synonymous, it doesn't mean that all nudity is porn. Anime such as Berserk, as well as many of the works by Satoshi Kon (Paprika, Tokyo Godfathers) show breasts, but they only have a short glimpse, and don’t follow the “OMG LOOK AT THESE BOOBS!” example set by ecchi animes.

For example, in Elfen Lied, when the character Nana is chained to a wall, stripped naked and covered in blood, it isn’t to get a rise out of the male viewers, but to strike a nerve and make you feel sorry for her condition.

Ya you thought this was gonna be fun and games didn't you.

Basically you can't call all nudity in anime fanservice, just as you can't call naked statues and paintings by artists pornography. Serious business out of the way, fanservice can be very entertaining.