Each of the Lyoko Warriors has an Avatar. Jeremie's Avatar has not yet been shown, though there has been much speculation amongst fans.
An Avatar is created by the Supercomputer whenever a new person enters Lyoko for the first time. (Before a person first arrives on Lyoko, the picture on their ID card shows a generic "person" icon.) Jeremie hypothesized in X.A.N.A. Awakens that the Supercomputer is able to do this by taking the subconscious desires of a person and projecting them in the form of an Avatar.
An Avatar contains information about the person's Life points, weapons, etc. Avatars contain the Lyoko Warriors' ID Cards as well. Avatars, according to Jeremie in Revelation, are stored within the restricted access part of the Supercomputer, so their minds can't be directly possessed by X.A.N.A. unless their programming was modified.