Emotions are a shorthand way of expressing various emotions with one or two words. Generally, these emotions will be seen by everyone in the same location as you. There are hundreds of emotes, and more being added whenever a player suggests a good one. An example of an emote would be SMILE, to smile (unsurprisingly) or SALUTE. Most emotes may be targeted at someone too. So you could, for instance POKE ROARK to poke Roark in the arm. Emotions run the gamut from the mundane to the sometimes silly (try TIGGER, for instance) and some players delight in trying to discover new ones.

So if, for instance, Roark typed FLUTTER ESTARRA, Roark would see:
You flutter your eyelashes charmingly at Estarra.

Estarra would see:
Roark flutters his eyelashes charmingly at you.

and everyone else in the room would see: 
Roark flutters his eyelashes charmingly at Estarra.

You can also emote at objects around you, for example, POKE ROCK. If you happen to be holding a rock, and you want to poke a different rock in your room, you can POKE ROCK HERE. The 'here' modifier means to ignore your inventory and target only objects in your room.

A list of emotions may be found using the commands outlined in HELP EMOTIONLIST.