ELI5 Tesseract - what is it and what does it look like?

What is the tesseract? The geometric shape, not the fictional Marvel space stone! How can we visualize a 4D shape in a 3D world? What did the great Carl Sagan say about why it’s so hard for us to imagine 4 dimensions? Who discovered the tesseract in the first place?
... we explain like I'm five
Thank you to the r/explainlikeimfive community and in particular the following users whose questions and comments formed the basis of this discussion: lifewitheloise, portarossa, geetarmikey, green_meklar, sabertoothedpudding and okami31
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