What do altars in the Old Testament foreshadow in the New Testament?

Answer:

"Do not be carried away by varied and strange teachings; for it is good for the heart to be strengthened by grace, not by foods, through which those who were so occupied were not benefited. We have an altar from which those who serve the tabernacle have no right to eat. For the bodies of those animals whose blood is brought into the holy place by the high priest as an offering for sin, are burned outside the camp. Therefore Jesus also, that He might sanctify the people through His own blood, suffered outside the gate. So, let us go out to Him outside the camp, bearing His reproach" (Hebrews 13:9-13).

Under the Old Law, only the priests were allowed to partake of the sacrifices. "Then the LORD spoke to Aaron, 'Now behold, I Myself have given you charge of My offerings, even all the holy gifts of the sons of Israel I have given them to you as a portion and to your sons as a perpetual allotment. This shall be yours from the most holy gifts reserved from the fire; every offering of theirs, even every grain offering and every sin offering and every guilt offering, which they shall render to Me, shall be most holy for you and for your sons. As the most holy gifts you shall eat it; every male shall eat it. It shall be holy to you'" (Numbers 18:8-10). However, Christians partake from an altar that the Levitical priests had no right to.

Jesus is our High Priest as well as the one sacrifice offered for sin (Hebrews 10:10,19-22). Each Christian serves as a priest before the Lord (I Peter 2:5) and thus, we partake of the sacrifice of Christ. Thus, in this sense, the altar for Christians is the cross of Christ.