Okay, I'm no techno wizard, but here's my best attempt to explain it. Parallax is the apparent movement of the reticle in relation to the target when your eye moves from side to side or up and down behind the scope. Lets say you're looking at a target 300 yards away and you move your head side to side a little bit and notice the reticle doesn't stay exactly on the same spot. That's parallax. Scopes without adjustable objectives will generally be parallax free at 100 or maybe 150 yards. So, if you're looking at a target at that distance and move your head around behind the scope, the reticle will stay on the exact same spot. Adjustable objectives allow you to change the distance at which the scope is parallax free. For the average guy who's not going to ever shoot anything over 250 yards or so an adjustable objective is not needed because parallax is pretty much a non issue out to that distance.

You can probably find a better explanation of parallax at any of the scope manufacturer's websites.