In general a covering, wrapping, sometimes a curtain. . . .

Separating the holy place and the Most Holy Place (Ex 26:31-35) was a veil made of blue, purple, and scarlet material (v 31), with figures of cherubim, representative of the angels about God's throne. The veil in the ancient tabernacle, and later the Temple, veiled the presence of God from the priest as he stood before it ministering the sacrificial blood and burning incense upon the golden altar day by day throughout the year (see Lev 4:6; see also Sacrifices and Offerings). This was as close as anyone could approach the Divine Presence, except on the Day of Atonement (ch 16:2, 12, 15, 16; cf. ch 21:21-23; see Atonement, Day of). Because of its proximity to the ark of the testimony the veil was sometimes called "the vail of the testimony" (ch 24:3), or "the vail, which is before the testimony" (Ex 27:21). When transported from one place to another, the ark was draped with this veil (Num 4:5). At the time of Christ's death the corresponding veil in the Herodian Temple was rent from top to bottom (Mt 27:51; etc.).

In the LXX the veil separating the two apartments of the ancient sanctuary was called katapetasma, a name given also to the curtain at the door of the tabernacle; hence, apparently, the designation "second veil" for the inner curtain in Heb 9:3.

Heb 10:20 speaks of our Lord's ascension to heaven in the likeness of humanity as consecrating "a new and living way, through the veil, that is , his flesh," by which we are enabled to "draw near with a true heart in full assurance of faith" (vs. 20, 22), entering into the Divine Presence through faith. The Christian's hope, the apostle further declares, enters "into that within the veil; whither the forerunner is for us entered, even Jesus" (ch 6:19, 20) -- Seventh-day Adventist Dictionary.