Information from Wiersbe's Expository Outlines of the Old Testament and Coffman's Exodus Commentary.

Old Testament Significance
New Testament Lessons
Ark of the Covenant

Mercy Seat

A symbol of God's law, the Ark was made of wood covered with gold. The Ark was the throne of God where His glory rest on the Mercy Seat (top), a symbol of His mercy. The sacrificed blood was sprinkled on the Ark to cover the sins of the people. The phrase "Mercy Seat" also means "propitiation." Jesus is the propitiation for us today (Romans 3:25; I John 2:2.) His blood was shed to cleanse our sins. We come to God through Him and offer our spiritual sacrifices (I Peter 2:5,9).
The Inner Veil The Inner Veil hung between the Holy Place and the Holy of Holies and was passed only once a year by the High Priest on the Day of Atonement (Leviticus 16). Hebrews 10:19-20 teaches that this Veil represents Christ's body which was given for us on the cross. When He offered up His spirit, the veil in the temple was torn from top to bottom, thus allowing anyone to come at any time into God's presence (Matthew 27:50-51).
Altar of Incense Incense was continually burned at this altar that stood before the veil separating the Holy Place from the Holy of Holies. The High Priest was to make atonement on its horns once a year before entering the Holy of Holies. The Altar of Incense was a symbol of prayer. Christians are to be continually in prayer (Romans 12:12).
Table of Showbread A symbol of God's providence, the Table held the twelve loaves of bread that were a reminder that the tribes were constantly in the presence of God and that God saw all that they did (Leviticus 24:5-9). The bread also reminded the people that God fed His people. God provides what we need (Matthew 6:25-34). We as Christians are daily in God's presence. We are to "feed on" God's truth (Matthew 4:4). Jesus is the Bread of Life (John 6:35).
Golden Lampstand Symbolizing light from God, the intricately patterned Lampstand was to give light continually, fueled by clear olive oil (Exodus 27:20) Rev. 1:12-20 indicates local churches are represented by golden lampstands. Jesus is the light of the world (John 8:12). Christians are to be a light to the world, also (Matthew 5:14).
Bronze Altar The Bronze Altar stood in the courtyard of the Tabernacle. This is where the animals were sacrificed to cover the sins of the Israelite people. Jesus's death on the cross was the ultimate sacrifice for our sins. He is pictured in all the sacrifices God commanded Israel to bring (Leviticus 1-5; Hebrews 10:1-14).

Supplement to The Majesty of Christ - A Study of Hebrews, lesson 8