A metaphysical barrier between the mortal realm and the Fade. Neither spirits nor mortal beings can easily pass physically through the Veil, but the consciousness of mortal dreamers easily does so.
The Veil is weakened in places where a lot of death or use of magic has occurred and areas that can be seen or felt where the Veil is thin is called a Veil Tear. Mending the tears in the veil is said to be extremely difficult, if not impossible, however it has been accomplished. Sophia Dryden (or what is left of her) and Avernus both seem to be able to strengthen the Veil at Soldier's Peak, but the thinned Veil in that place seemed to have been caused by Avernus in the first place in a controlled manner, so it's hard to say if the sealing skills they used would have worked in a place such as the Brecilian Forest. The Warden has managed to mend Veil Tears in both Awakening and Witch Hunt.
The Veil is not an object; it cannot be touched or seen. It is a metaphor used by mortal scholars to explain the interactions between the two different realities.