Here's a simple analogy: You want to class data in a 2D plane by drawing a straight line and saying everything on one side is in one class. But there's not lik

Here's a simple analogy: You want to class data in a 2D plane by drawing a straight line and saying everything on one side is in one class. But there's not likely to be a line that does this in general. So you assign a z coordinate to all your points (even randomly). And it's now much more likely that at plane divides them the way you want than a line did before, as there are many ways to slip a plane in between the groups that wouldn't have been possible with a single line in the 2D plane. Swapping the inner product for another inner-product-y kernel is similar, but with many / infinite dimensions coming into the picture.