Warning: Spoilers. Do not read if you haven't seen the entry you are going to read.
Jessica apparently puts on a happy demeanour but seems to be privately bothered by her memory loss and insomnia. She is also an assertive individual, perfectly willing to initate confrontations, such as calling Jay out on his repeated change of stories. She seems observant and intelligent, deducing after observing his behavior that Jay may be suffering from the same memory loss that she is. One time she is seen talking on a cell phone while Jay is coming home with some supplies, this implies that she either still has contacts with the outside world or she was pretending to talk on the phone to have the opportunity to talk to Jay. She also mentions that Jay's name sounds familiar when they first talk.
There are two main schools of theories about Jessica right now: that she is also suffering from similar "slender sickness" as Jay and that they may have teamed up during Jay's seven month period of memory loss, or that she's a plant sent by Masky and/or totheark to spy on Jay and to further control his priorities.
Some people also speculate that she is the unnamed, unseen camera woman in Entry 12 or the unnamed, unseen, unheard woman in the backseat of Entry 9 but there is evidence against this, as Jessica has implied that she is a native of the area the Jay appeared in after Entry 27 and in Entry 22 Alex mentions everyone in the cast and crew of Marble Hornets after they disappear.
It is important to note, as this confusion comes up regularly, that Jessica bears no resemblance to Amy, the camerawoman in Entry 26, who is implied to be Alex's girlfriend. Amy is clearly seen in the footage of entry 26, and is a straight-haired, blond, round-cheeked woman with a short, button-like nose. Jessica is not.
In this video, http://www.youtube.com/watch?v=ysgQ9spsphk&list=UUmdNkTwloAtGK-HHVCK-VFA&index=3&feature=plcp, a 'classified' recording of an investigation between an officer and a father takes place. The father, Thomas Nealy, reported his daughter went missing in the woods behind their house. The daughter's name is Jessica Nealy, and in the video her captive is described to have an appearance not unlike that of Slender Man. Seeing as how this was in 1989, the possibility of the girl being Jessica from the Entries is not impossible, although our Jessica appeared to be younger than that would make her.