Agender (or a-gender) is a term used to refer to people who do not identify with any gender. There is a lot of debate over the proper terminology for such things, but in general, agendered people do not attempt to act in male or female roles, but do not see this as necessarily having anything to do with their bodies or their sexual orientation. In other words, you can be agendered without being asexual or aromantic and without making any particular attempt to appear androgynous.
While definitions vary, agender is essentially a general term that covers people who do not identify with any defined gender role. Roughly, the taxonomy goes something like this:
There is no real way to describe how an agendered person will look or act, other than the broad generalization that they are unlikely to wear much makeup or gender-linked clothing (skirts, ties), and are not likely to act masculine or feminine. Being agendered does not mean that you will not be attracted to someone who is macho/feminine, nor does it mean that you will act significantly different than anyone else; after all, there are lots of normally gendered women who don't love Sex in the City and lots of normally gendered men who don't like football. An agendered person is simply someone who feels that the entire complex of socially constructed gender doesn't apply to them. This feeling may or may not be accompanied by gender dysphoria, a feeling of depression or discontent related to their unusual gender.
For the most part, I have followed the definitions found at Neutrois.com, which is an excellent site for further reading. More generally, Wikipedia has a Trangender Portal which is worth exploring.