How do I explain Jesus to a Jew?
I would explain how Jesus fulfills Old Testament prophecies regarding the Messiah and the people of Israel, though I would use the term “Hebrew Bible” in speaking to a Jewish friend.
For example, Jesus fulfills the “suffering servant” prophecy of Isaiah 52-53, in which a lamb is described as taking on the sins of the people, and not just of the Jewish people but the whole world.
Indeed, Isaiah prophesied elsewhere that from the root of Jesse would come an ensign for all nations (Is. 11:1-10), a reference to Jesse’s son, King David, whose dynasty had fallen but would one day be restored in Jesus (see Luke 1:31-33). The prophet Amos affirmed that the fallen house of David would one day be rebuilt and that the nations would be drawn in (Amos 9:11-12).
In addition, God told Abraham that all the nations of the world would be blessed by his descendants (Gen. 22:18), a prophecy again fulfilled in Jesus.
That’s a good start. Just remember that the Church teaches that Catholicism is the fulfillment of Judaism; it is the new Israel, and we consistently see that theme played out in Church life and teaching, e.g., the twelve apostles fulfill the role of the twelve tribes of Israel, and the Mass is the New Covenant fulfillment of Passover, in which we not only offer anew but partake of the Lamb of God (Luke 22:19-20, John 6:47-59, Ex. 12).