They are cubic graphs that don't admit a proper 3-edge coloring, in other words, 3 edges meet at each vertex but you need four colors to color the edges so no two edges with the same color meet at a vertex. 

/me goes off hunting snarks

I found one! (The Petersen graph, which you knew about already)

Please tell me there's a class of snarks called boojums?

Well, they were both named by Martin Gardner. A boojum would be a planar snark, but their existence would contradict the four color theorem. So the set of boojums is empty (could explain why they are so hard to find).

I guess if someone did find one, the foundations of mathematics would swiftly and silently vanish away