Platonic solids are 3D shapes. A platonic solid is constructed out of congruent and regular polygonal faces.
This means that all the polygonal faces have the same size and shape (congruent) and the angles and sides of those faces are the same (regular).
Furthermore at each vertex the same number of sides meet.
Because of these unique properties mathematicians have studied these solids for thousands of years.
They are named after the philosopher Plato, who lived in ancient Greece. These solids are prominent in his philosophy. He thought that these solids made up our universe. He associated these regular solids with the elements: earth, fire, water and wind. Though there was a fifth regular solid Plato never really mentioned an element to associate it with. He just said it was what "...the god used for arranging the constellations on the whole heaven". It was another philosopher Aristotle who associated aether with the fifth platonic solid.
Euclid, a brilliant mathematician, whose work has been instrumental in the development of logic and modern science, completely mathematically described the 5 platonic solids in his book elements.