The wicked figuratively receive the just deserts of their evil deeds: the dregs of a bitter cup. The cup in ancient scripture was sometimes symbolic of experiences of suffering. Elder James E. Talmage wrote: “Our Lord’s frequent mention of His foreseen sufferings as the cup of which the Father would have Him drink (Matt. 26:39, 42; Mark 14:36; Luke 22:42; John 18:11; compare Matt. 20:22; Mark 10:38; 1 Cor. 10:21) is in line with Old Testament usage of the term ‘cup’ as a symbolic expression for a bitter or poisonous potion typifying experiences of suffering. See Ps. 11:6; 75:8; Isa. 51:17, 22; Jer. 25:15, 17; 49:12.”44 Compare also 3 Nephi 11:11.
“Dregs” are sediment, the bits of matter that settle to the bottom of a container of liquid; they are the worthless, least desirable part.