"Agendered" describes a transgender person who does not have a gender, or lacks a gender identity.
An agender identity falls under the broader transgender category of "Genderqueer," yet unlike other more gender-fluid or third-gender categories of genderqueers (such as Androgyne, Bi/trigender, Polygender, Third gender, genderfluid etc.), an agender identity has no identification with any gender, or lacks a gender identity; Such people could be said to be gender-neutral.
Agendered people may or may not experience body dysphoria, and may or may not have or seek access to various forms of body modification (hormones, surgery, etc.). An agendered person who seeks to alter their body to be gender-neutral is frequently termed a "Neutrois" (pronounced "nu twa".) Additionally, agendered people may or may not express characteristics labeled femme or butch, but such expressions have no bearing on their gender-less identity itself.
An agender person does not conform to the social construction of gender. This identity falls under the non-binary umbrella. Agender people may use any pronouns they are comfortable with. Please respect them.
A person who identifies as agender is one that identifies as neither male nor female. This is in contrast to cisgender people, who identify as the sex that is the one that they originally physically were, and transgender people, who identify as a specific sex other than the one they physically were, among other identities.
Some agender people have preferences for certain personal pronouns. While most people prefer either he or she, which some agender people prefer or don't mind, others prefer "they", "it", or a not-well-known attempt at making a new pronoun.
The argument for "they", as I understand it, is that it is sometimes already used as a singular word (such as for a person of unknown gender and sex), but others prefer "they" remain plural. The reasoning for preferring "it" can be the person rejecting or ignoring the diminutive uses of the word, at least when it is used tastefully. Other times, both of those are found to be insufficient, so additional word choices are found or created.