The basic significance of the clothing of the high priest and the other common priests was the concept of separation in that they were separated, sanctified or set apart, for divine use. The common priests had a more modest type of clothing, and the high priest had a very special type of clothing.
The significance of the clothing of the priests was twofold. First, it emphasized the holiness of God. Secondly, it signified the need for an intermediary in that no Jew was free to go up to the Tabernacle, offer his own sacrifice, then walk into the Holy of Holies to sprinkle the blood. He needed the priesthood of Israel to do all this for him. The whole priestly system symbolized the need for a mediator between God and man. While the prophets represented God to man, the priests represented man to God. This is what Jesus became to us after His ascension.
Romans 8:34
Who is he that condemneth? It is Christ who died, yea rather, who is risen again, who is even at the right hand of God, who also maketh intercession for us (KJV).