The Veil is an astral, incorporeal state of existence on Earth, which incorporeal and invisible spirits and entities such as ghosts and reapers exist in. The Veil and the entities in it are usually invisible to humans on the physical plane, though some supernatural creatures such as demons and angels can naturally pierce into and perceive the Veil.
All ghosts exist within the Veil, as do reapers in their natural incorporeal state, and demons such as Alastair can also confine their smoke form's manifestation so that it's apparently only visible in the Veil. (Death Takes a Holiday) Demons also know of an invisible ink which can only be seen in the Veil. (Death Takes a Holiday, Abandon All Hope...) It has been implied that hellhounds, when on Earth, exist in the Veil to some extent (in that this is the reason hellhounds on Earth are invisible to those unable to pierce the Veil), as do demons' true forms to some extent; as in the latter case, humans able to pierce the Veil can perceive demons' true faces beyond their vessels', (No Rest for the Wicked) but ghosts in the Veil apparently cannot. (Death Takes a Holiday)
The Veil is a limbo-like, incorporeal state of existence, in which one is usually invisible and incorporeal to the physical world and the things in it (excluding certain people and supernatural beings capable of piercing and perceiving the Veil). However, spirits and entities within the Veil such as ghosts and reapers can still influence the physical plane to a limited extent; in that their presence can cause electrical and temperature flunctuations, and ghosts can learn to physically and telekinetically interact with and even make themselves briefly visible on the physical plane. Beings in the Veil are able to perceive each-other, (In My Time of Dying onwards) although still can only touch each-other by learning to physically interact with each-other in the same manner as with corporeal beings. (Death Takes a Holiday)
It has been implied that when spiritual supernatural beings such as demons and angels gain physical form on Earth via possession, their true forms exist to some extent in the Veil while they are on Earth; their true forms can be seen beyond their vessels' faces by humans able to pierce the Veil, but apparently not by ghosts within the Veil. (No Rest for the Wicked, Death Takes a Holiday)
There are several means of either 'piercing' the Veil so as to be able to perceive the invisible entities in it, and even of actually entering and becoming a denizen of the Veil. Angels and demons can naturally pierce the Veil, allowing them to see reapers in the Veil and to easily recognise other supernatural beings. (Death Takes a Holiday onwards) When the contract of a human who's sold their soul to a demon is about to expire, that human can pierce the Veil and see demons' true faces as well as hellhounds. (Crossroad Blues, No Rest for the Wicked)
Humans can enter the Veil through several methods, most of which apparently involve them leaving their physical bodies and becoming ghosts. If a dead human stays behind on Earth rather than moving on to their afterlife, then they will exist within the Veil as a ghost until they are either vanquished from the world of the living or are transported to one of the afterlife realms. Humans' spirits can also temporarily leave their bodies and exist within the Veil, via astral projection or near-death experiences. (In My Time of Dying onwards, Death Takes a Holiday) It was also claimed that rogue reapers such as Ajay know secret portals and backdoors into and out of the Veil among other realms. (Taxi Driver)