“Redeem means, (1) To buy again something that has been sold, by paying back the price that bought it. (Lev. 25:25;27:20)(2) To deliver and bring out of bondage those who were kept prisoners by their enemies. (Deut. 7:5;32:6) Cruden’s Concordance of the Bible. Jerusalem had been sold, figuratively speaking, by the apostate Jews. They had perverted the ways of the Lord, and, too, they had abandoned the covenant their fathers had made with the Lord at Mount Sinai. The land of Jerusalem was the land of their inheritance. The Mosaic Law provided that land which had been sold, among other things, could be redeemed. However, a price was demanded for its redemption.…There was only One who could meet the prescribed terms. That One was their King! Isaiah said, ‘He hath redeemed Jerusalem’; not with money or with the might of a great army, but He hath Redeemed it with the blood that was shed on Mount Calvary; the Redemption brought about by Jesus of Nazareth, the King of the Jews.” (Reynolds and Sjodahl, Commentary on the Book of Mormon, vol. 2, p. 130)
In addition to its spiritual redemption, The Old Jerusalem is not fully redeemed until the Savior comes amidst a vicious battle between the Jews and a group of nations from the north. After a 3.5 year siege of Jerusalem, the Savior will come to redeem them from their military enemies (Rev 11:2, Zech 14:2-3). As mentioned above, He will also come to declare spiritual redemption to those who should have known that he is the Messiah.
Elder George Q. Morris
"’Break forth into joy, sing together ye waste places of Jerusalem: for the Lord hath comforted his people, he hath redeemed Jerusalem. The Lord hath made bare his holy arm in the eyes of all the nations, and all the ends of the earth shall see the salvation of our God.’ (Isa. 52:9-10.)
“And this looks to the time when the Lord Jesus Christ is to stand on the Mount of Olives, and the people will gather about that mount, and they will say, ’What are these wounds in your hands and in your feet?’ And he will say unto them, ’These are the wounds received in the house of my friends.’ Then they will recognize him--Jesus Christ, the Savior of the world.” (Conference Reports, Apr. 1960, p. 101)