Clogging is an informal game term. Your hand gets "clogged" when it's full of cards you cannot (or do not want to) play or discard. If your hand is clogged up, you draw fewer cards when you reconcile in the Regroup Phase, so you're slower to set up your Fellowship on the Free Peoples side and draw fewer minions to play for your Shadow side.
Choke strategies often clog up the opponent's hand, by limiting the amount of Twilight available to your opponent. With little Twilight, they can't afford to play as many Shadow cards. This doesn't just weaken their Shadow phase, but also weakens their Free Peoples gameplan, because those Shadow cards clog up their hand when they reconcile.
Wraith culture is infamous for clogging up the hand, because their minions are generally fairly expensive and often have situational abilities.
Your hand clogs up when you don't cycle well.