lit. 'something which one grasps, to which one clings, i.e. the 5 groups of existence (khandha, q.v.).
In the suttas, the word is mostly used in such expressions as "One of the 2 fruits may be expected: either perfect wisdom or, if the groups are still remaining (sati upādi-sese, if there is a remainder of groups), Anāgāmīship" (D.22).
Further (A.IV.118): "Here the Perfect One has passed into the Nibbāna-element in which no more groups are remaining (anupādi-sesa)." Cf. nibbāna.