According to Wikipedia:
“A gömböc […] is a convex three-dimensional homogeneous body which, when resting on a flat surface, has just one stable and one unstable point of equilibrium.”
What does that mean? Well, it’s kind of like a self-righting roly-poly toy, except that it isn’t weighted; it’s of uniform density throughout. But however you put it down, it rolls back to its stable equilibrium position. (Unless you put it down very carefully in its unstable equilibrium position, in which case it stays there until disturbed.)
About the name, Wikipedia says:
If analyzed quantitatively in terms of flatness and thickness, the discovered mono-monostatic body is the most sphere-like body, apart from the sphere itself. Because of this, it was named gömböc, meaning a diminutive of gömb ("sphere" in Hungarian). Originally gömböc is a sausage-like food: seasoned pork filled in pig-stomach, similar to haggis. There is a Hungarian folk tale about an anthropomorphic gömböc, which swallows several people whole.
Apparently some tortoises have somewhat gömböc-like shells, allowing them to right themselves more easily.
You can purchase a gömböc in a variety of materials from the Gömböc Webshop, but they have to be made with very fine tolerances to work properly, so they’re pretty expensive—on the order of €300.