Caption: Animations showing from 2 different directions a tesseract being rotated in 4-dimensional Euclidean space projected into 3-dimensional Euclidean space.
Features:
Note the following well known hypercubes with special names: point (0-cube), line segment (1-cube), square (2-cube), and, of course, cube (3-cube) (see Wikipedia: Hypercube: Elements).
The projection of a 4-dimensional shape into a 3-dimensional Euclidean space (i.e., 3-dimensional hyperplane) is a 3-dimensional shape.
Humans can understand 3-dimensional shapes thanks to stereopsis, experience, imagination, and lots of other things (see Wikipedia: Stereoscopy: Background).
It's all pretty tricky to analyze, but we mostly do it pretty easily. We can be fooled by optical illusions, of course.
If the tesseract were NOT rotating, it would just be a somewhat unusual 3-dimensional shape.
The rotation in 4-dimensional Euclidean space makes the projected shape morph.
See Wikipedia: Tesseract for a fuller description of the animations.