Tenpai names a hand for which one additional tile is enough to form four groups and a pair, or a valid special shape. In shanten terms it is zero-shanten, the last step before a win. The tile types that would finish it form its wait (machi), and their available copies make up its ukeire.
You reach tenpai the moment your hand needs only one more tile to satisfy a winning structure, whether by drawing it (tsumo) or claiming a discard (ron). A closed hand in tenpai may declare riichi; an open hand cannot, but can still win if it holds a yaku. Common wait shapes include ryanmen, kanchan, penchan, shanpon and tanki, each with its own ukeire count.
Tenpai is the goal of most of the hand: everything before it is about lowering shanten efficiently to arrive ready before your opponents. At an exhaustive draw (ryuukyoku), only players in tenpai collect the noten penalty payments, so reaching tenpai carries direct scoring value. Beware furiten: if your winning tile already sits in your own kawa, you cannot ron and are limited to tsumo.