It may not have the iconic value of Pooky, or Garfield's box-bed for the public at large, but Jon's obsession with his own sock collection, and association of his dedicated sock drawer with the most intimate aspects of his life is well documented in Garfield. Overlooking the obvious weirdness of the premise, Jon's sentiment is a little heartening, because it shows that some part of him is trying to stay even-keeled on the subject of Liz. Given the excitement of any new relationship, compounded with Jon's extraordinary circumstances of loneliness, the overzealousness he's demonstrated already is being surprisingly well tempered by sweet concern for Garfield's feelings.
The Garfieldian thing to do is for Jon's happiness to, well, ruin his own happiness; the easy way would be if Jon smothered Liz with too much attention. This strip takes a trickier tack: Jon's idea of maintaining personal boundaries is confused and a little neurotic. While the sock drawer is a more intimate than public space, it's also a boring, commonplace space. So the Dear Abby advice we imagine when hearing Jon's version of privacy is nothing compared to the scene Garfield visualizes/ knows is coming. When Jon finally presents his sock drawer to Liz with some pride and a little embarrassment, I can only imagine she would not care at all. Disinterest in a man's sock drawer will be the unkindest cut of all.
Besides the mild perversity of Jon's fixation on his socks, the backbone of the joke is that even when Jon is ready to open up, there may not be much to reveal. The Garfield in us explains: Jon is boring. A happier explanation, and the reason Liz ultimately likes Jon: he has nothing left to hide, because he wears his heart on his socks. I mean "sleeve."