growing up

the story starts with a very tiny dot, a tiny wee thing that only really exists in your imagination and has a dimension of 0 - because there's nothing at all to measure
it barely exists.

the point goes for a short walk, the trace of where it walked is a straight line and this has dimension 1 (its length)

the line now goes for a walk and this time leaves a trace of where it went that has 2 dimensions (length and width)

if this square goes for a walk the trace is a 3 dimensional shape (a cube - or a cuboid with a square end)

the cube goes for a walk, its trace is a 4 dimensional shape called a hypercube or tesseract
it can be drawn in 2 D by drawing a cube close to another identical cube and then join all the corresponding corners

there is a neat video by Albert Renshaw, showing how to construct a tesseract








and so on ......