Backings in general allow you to use a less than perfectly grained wood for the belly side.
A hickory backing is as Marc said, a thin strip of (typically although not always) quartersawn hickory. It works because the grain is very straight and the grain runoff is minimal.
Yes you can make your own backing. You just have to be able to read the grain well, select a good quality board, carefully resaw, and thickness to the desired dimension. No different than resaw ing any other thin lamination except the grain is critical, and the thickness needs to be even.
If you have a table saw or bandsaw and a planer or thickness sander (or even just a hand saw and hand plane if you're skilled) then you can make backings. In the old days this is how they would make veneers; as they say, where there's a will, there's a way.
I have not bought backings in a long time and I suspect neither has Marc.
Step one, find a good hardwood supplier who will let you go through the stacks of hickory.