There's one phrase that is commonly used to describe Samhain, and that is "the time of year when the veil is thinnest."
Let's start with the basics here - what exactly is the veil? In this context, the veil is what 'separates' this world from the unseen world. Many traditional witches will use the term hedge instead of veil, which might help paint the picture. A hedge is a boundary between one thing and another - such as the tame land of the yard and home, and the wild land of the forest... or, the seen world, and the unseen world. The veil is that boundary, that separation between the two.
This is not a hard boundary. As an example, think of a typical bridal veil. It's there, you can see it, touch it... but it's often thin, gauzy... you can see through it, air passes through it easily, water would too. If the veil is a few layers thick, it might take some time for water to pass through, but it would - if it were just one thin layer, the water would pass through quickly and without issue.
Of course, calling it a boundary may bring about the wrong impression.
The unseen world is not just a separate location - as a backyard might
be from the woods - but it is interwoven throughout the seen world, as
well. We're just not usually aware of it. The veil, the boundary, is not
really an actual block between the two, but more of the limit of our
So why is the veil said to be thinnest at Samhain? One reason often given is that Samhain is the peak of the dying season, and it's that transition that causes the veil to thin. I like this imagery myself, but I don't think that's the complete answer.
There are other times of the year when the veil is said to be thin - many associate Beltaine with another thin spot, as it is the peak of the "birthing" season. It's not just death that thins the veil, after all. Beltaine, along with Litha/Midsummer in some cultures, are classically times when the spirits are quite active - although they became more associated with fae and other such spirits as opposed to the dead that are associated with Samhain. Of course, the dead are not only associated with Samhain, because we see things like the Wild Hunt of Yule/winter in many European cultures. The Greeks thought the restless dead wandered with Hekate on the last day of every month (what we would now call the new moon). Other cultures have their own, different views.
So what is it really that causes the veil to thin? I don't know that it is really anything external, like the changing of seasons, at least not in itself. I think a big part of it rests within the human mind. These symbols, these expectations and ideas of a society, they stick right into our subconscious and they change our perception. If you're in a culture where the dead wander every new moon, that will influence your perception of the veil accordingly.
Likewise, if you're in a culture where Halloween is that spooky time, where horror movies and ghost hunting shows take over the TV, where people start sharing their stories, going to haunted houses, putting on costumes, putting out decorations, etc. that cultural belief is, again, going to influence your views and perception.