As of a few hours ago, all I know about quandles was that they had something to do with knots. Since in our modern connected age ignorance lasts only as long as you want it to, I decided to find out more. I found this slide deck by Bob McGrail explains both the definition of quandle and the motivation in knot theory in a measly six slides. (The rest of the talk is how to efficiently compute quandles.)

Sam Nelson has a nice introduction to the general area of universal-algebraic invariants from the Notices, called Revolution in Knot Theory. Nelson also discusses the emergence of virtual knots.