The veil obstructed entrance into the Holy of Holies (variously translated "the Most Holy Place," "the Holiest of All," "the sanctuary"); and that place symbolized the presence of God. The rending of the curtain (Matthew 27:51) signified the end—or, the destruction—of the Old Covenant way of access to God. The tabernacle, the priesthood, and the ritual taught that God was inaccessible—that He was remote.
In fact, the ritual taught that access to God was restricted to everyone except one man, once a year. Nobody else had access to God. The only one who actually had access, according to the ritual, was the high priest; and he went into the Holy of Holies with a great deal of fear—that one day of the year, on the day of Atonement.