We'll look at two hold 'em hands to see the difference between a situation where you should bet and another where you might consider checking. In both cases there is a medium-sized pot:
With two jacks you should bet in an attempt to win the pot right there, even if you think only a better hand will call. If you give your opponents a free card (with what would have been the best hand) and an ace, king, or queen falls on fourth street, you are clearly in trouble. Thus, you don't want to give your opponents a free chance to draw one of those cards to make a higher pair than yours. Even if an ace, king, or queen doesn't make an opponent a higher pair, your checking on the flop gives anyone the opportunity to bluff you successfully if one of those cards falls.
With aces you can give serious consideration to checking on the flop. Having two aces instead of two jacks has not significantly affected your chances of having the best hand since we'll assume that in both cases there has been no reason to think you are up against two kings or two queens in the hole. With two aces, however, you are not worried about as many fourth street cards as you would be with two jacks, and so you might as well check just in case someone has made three l Os. Assuming no one has a 10 in the hole, an additional benefit of your checking your pair of aces is that you have disguised your hand. Not only do you
not fear a king, queen, or ace falling on fourth street (as you would with a pair of jacks), you would welcome it, since any of those cards, as well as a jack, might give an opponent a playable second-best hand.