It’s an object with higher dimensions than a normal object.
For example, a normal object has only three spatial dimensions: length, width, and height. These are the three dimensions of ordinary space.
But it’s possible to imagine a space with 4 dimensions. The 4th spatial dimension would have to be perpendicular to the other three. That means you wouldn’t be able to see it in 3-space. Only a portion of it that was super-imposed (like a projected image) on 3-space. We can mathematically describe it, but not directly see all of it.
This can be seen in lower dimensions more easily. What does a cube look like in 2 dimensions? Well, it depends on the angle, but kinda like a square. You see this in the real world all the time with shadows. The shadow of a 3d object is a 2d projection of it.
So a tesseract is more than 3 dimensions and we can only see a shadow of it in 3 space because we aren’t capable of sensing higher dimensions directly.
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