So first, let’s talk about chiral shapes so that definition is covered. Your left and right shoes are chiral mirror images of one another, since they are clearly like one another, but there’s no way to rotate them to make a right shoe turn into a left shoe. Another example, this time of a 2D chiral object, would be a spiral. A spiral spins either clockwise or counter clockwise, and no rotation in a 2D space can change that. You need to rotate the spiral in a 3rd dimension to get it to become its mirror image. You might do the same to a shoe, but you’d have to rotate it in a 4th dimension since it’s a 3D object.

So a good test of orientabilIty is this: take a lesser-dimensioned chiral shape and traverse it along the shape of choice. If there exists no traversal which can make the chiral object look like its mirror image, then the shape is orientable. This can also be said as the shape having clockwise and anti-clockwise as distinct directions. Both the Möbius strip and the Klein bottle are non-orientable because they can convert lesser-dimensional chiral objects into their mirror images.