With the seance room as the point of reference, a 'thing' that appears within the room is an apport. A 'thing' that disappears from the room, and which may or may not be later discovered elsewhere, is an asport.
The 'thing' in question is not, in itself, a supernatural object. Usually it's small; a pebble, a flower, an ornament. Because the object is small, it's easy to accuse the medium of having concealed it, and it's also easy for a fake medium to conceal such an object.
If the apport is, for example, a rose, and it's later discovered that the neighbour's rose bushes have been clipped in the night, then there's a good chance of some fakery going on. Note I said 'a good chance'. If the medium asked for a rose, why would any spirit travel further than the nearest rose bush to get it? Yes, it's highly likely to indicate that the medium, or an assistant, merely leaned over the fence, but it's not proof of that.
There have been cases where a particular object was apported from the sitter's own home to the medium's. Objects marked secretly by investigators have appeared. Apports and asports are easily faked and often are, but real instances do occur. Poltergeists sometimes seem to throw things through walls; an object from the next room might appear, usually at speed.
How can a spirit move something through solid walls? How can they move things so quickly, despite the obstacles and distances often involved? One good discussion of the theories concerning this is here. The article mentions other instances of 'moved objects', including the Philadelphia Experiment (which must remain unconfirmed for now) but also definitive, reported science such as the levitation of objects and even animals in magnetic fields. Yes, that happened and was reported in scientific literature.
The article considers 'vibrational states of matter' as a likely means by which solid objects might be transported through walls. Well, maybe. I prefer the dimensional explanation. Of course, no definite explanation exists, so it's still a matter of which theory you prefer.
We live in three dimensions (I don't regard time as a dimension since I can't move freely within it. I refer only to spatial dimensions here).
Suppose you came across a world of two dimensions. You don't have to imagine this. Just get yourself a piece of paper and draw a two dimensional world. Lines represent the walls of houses. Your two-dimensional creatures cannot see or pass through these walls, no more than you can pass through the walls of your own home.
Your invented creatures cannot see you. They are unaware of your presence unless you act within their world. They have no concept of 'up' or 'down', and no means to look in those directions even if it occurred to them to try. Yet you can look down on their entire world.
Now, suppose your two-dimensional creatures gather in one room and have a seance. You're amused by this. You decide to liven things up for them, so you take an object from a room, far away from the seance, and drop it into the seance room.
The creatures are astounded. The object has disappeared from one place and reappeared in another, passing through solid walls on the way. From your point of view, the object hasn't passed through anything. You simply lifted it out of the two dimensional world at one place and put it back somewhere else.
Now (and this is the difficult part) move the experiment up by one dimension. The observer now lives in a four-dimensional world and is examining, and interacting with, a three-dimensional world in exactly the same way.
The four-dimensional observer cannot be seen by the three-dimensional creatures. They have no concept of which direction to look, and no means to do so should it occur to them. The observer can move an object from one place to another, with no concern over obstructions between those places because from the observer's point of view, there are no obstructions. Merely three-dimensional lines on three-dimensional paper.
Physics considers the possibility of more than three dimensions as almost a necessity for their calculations of the world to work. Currently, it seems we live in 11-dimensional space, but we can only see three of them. The other dimensions are usually explained as 'rolled up too small to see'.
Well, where's the third dimension in that two-dimensional world we've just considered? Is it the thickness of the paper, or perhaps the thickness of the lines drawn on its surface? From the perspective of the two-dimensional creature, that third dimension is irrelevant. It's invisible to them.
They might say, if they theorise about it, that the third dimension is 'rolled up too small to see'.
So, just because we cannot visualise a fourth, fifth or eleventh dimension from our frame of reference, does not mean that they contain nothing. To insist they are uninhabitable is to become like those two-dimensional creatures who scoff at the notion of our three-dimensional world.
The Celts imagined the world as a circle. Heaven was a larger circle, drawn around the circle of Earth. So, the living are contained within the circle of Earth and cannot see or visit the circle of Heaven. Those in Heaven can move freely within that circle, which includes the circle of Earth.
Surrounding this was another circle, which the Celts stated was only accessible to the Gods (when they became Christian they kept this image, but ascribed the outer circle to the Christian God. There was, originally, no Hell in Celtic thinking). So the Gods have a place nobody else can go, but they can move freely within Heaven and Earth because these are both contained within their circle.
The boundaries are not unlike those proposed by dimensional theory. If you live in three dimensions, you can poke and prod at a two-dimensional world and there's not a thing the inhabitants can do about it. They can only hope that when they die, they'll move from a two-dimensional existence into a three-dimensional one where they can hit you back.
Of course, if you're four-dimensional, they still won't be able to get at you.