The Covenant
The covenant is an 'agreement' between God and his people. Both Jews and Christians believes that though Moses the people entered a covenant with God. The terms of the covenant are summed up in the Ten Commandments.

The Lord said to Moses, 'Write these words down, because the covenant I make with you and with Israel is in these words.' So Moses...wrote down the words of the covenant, the Ten Words, on the tablets.

(Deuteronomy 11 : 26-28)

Jew's believe that the Israelites are God's chosen people, and this was ratified by the covenant which the Jew's still follow closely today. The covenant required faithfulness from the people to God, however, the nation failed and a new covenant was needed.  The prophet, Jeremiah, promised God would create a new, more improved covenant. 600 years later, at the last supper, Jesus indicated that day had come. Christians abide by the new covenant while the Jews do not because they do not accept Jesus as the Messiah.