Mormons feel a kinship of sorts with the Jews, as the descendants of the Israelites and whose beginnings we claim also as our own. Read, for example, this LDS article about how without Hanukkah there would be no Christmas.
We believe, in the LDS Church, that Jesus Christ instituted His church in its purity on the earth in different times and places through prophets among various peoples, and that one such instance is the restoration of the full gospel through the prophet Joseph Smith in the early 1800's. As taught in the Bible, we believe that before Christ's birth, Christ's followers sacrificed animals to think about Christ's sacrifice -which was to be the great and last sacrifice. After His crucifixion and resurrection, Jesus Christ instituted the sacrament to meet that purpose of remembering Him and committing to follow Him.
Some other commonalities between the LDS Church and the Jews historically are temples, prophets, priesthood, covenants, tithing, etc. The Book of Mormon is a record of Jewish people who left Jerusalem before it was besieged, around 600 B.C., and came to the Americas through God's guidance, and who, 600 years later, were visited and taught by Jesus Christ Himself following his crucifixion and resurrection.