Here Isaiah contrasts the general apostasy and sinfulness of the people with the atoning Messiah who takes away our sins. The phrase "the Lord hath laid on him the iniquities of us all" is very clearly a reference to the atonement. The reference to Israel as sheep turning away is an interesting set up of the next verse. The sheep in this verse are contrasted with the lamb of the next verse. Sheep and lamb are the same, and Jesus was a Jew. Nevertheless, his own turned against him. The symbolic significance of the lamb reference will be discussed after the next verse.
Variation: The Book of Mormon has "iniquities" in the plural, while the KJV has "iniquity" in the singular. While this may simply be a dictation error as I suggested with a similar occurrence earlier, Tvedtnes notes that the Hebrew term may be used as a collective, so that while it is grammatically singular, it may be legitimately translated as a plural in languages where the translated word is not a collective (Tvedtnes, John A. "Isaiah Textual Variants in the Book of Mormon." FARMS, 1981, p. 92).