It's hard to guess without experiencing the problem first hand but I would inspect the tires, if you see unusual wear on any or all tires, jack up the Explorer and check the wheel bearings for play, and the steering and suspension joints for excess play. Get this checked out it sounds like something has gross play and may render the Explorer unsafe to drive or may cause more wear or damage.
Do you feel the vibration more in the steering wheel, if so the problem is more likely in the front tires/suspension related. If you feel the vibration in the seat of your pants on the floor area then it may be drive line related. Worn U-joints usually squeak a little when they wear out.