This book states that "If a claimed tile is not taken within the next two opponents’ turns, i.e. before another two discards has been made, the player has a dead hand."
What is a dead hand, and how does it affect the game?
"Dead hand" has a few different meanings. It's hard to tell just from that one sentence, but it sounds like the one you're describing is the case where somebody forgets to take a tile, so their hand ends up short tiles (it's also a dead hand if the player forgets to discard and thus has too many tiles). A dead hand cannot be used to win the round, but the player still takes their turns as normal until the round ends.
"Dead hand" also sometimes refers to a declared mahjong that turns out to be invalid (like above, that player cannot win anymore, and play continues), or a round where all tiles are drawn from the wall and nobody makes mahjong, but neither seems to be what you're referring to in this case
The term "dead hand" is maybe ambiguous. The certainly most common use is for hands that may no further participate in the game due to a critical, usually accidental, mistake. This is related, but not identical to chombo (a usually intentional mistake by a player that ends the round and forces the offender to pay mangan).
The OP was referring to MCR rules. I am not very familiar with MCR, but to gain a basic understanding of the term, let me refer you to these (simplified) rules for dead hands in riichi mahjong:
I have found one other use of the term "dead hand", but I have never seen this elsewhere: