Not sure if you meant storing jigs while fishing or storage when not. In either case I use a plastic packing foam that's used for stuff that comes in the mail. For small jigs, I use a flat block of the stuff and use a razor or sharp knife to cut slits for the jig hooks:
I write on the lid of the box jig weights and hook size.
In my basement, I cut a
bar of the foam and insert hooks into it such that they are parallel to one another.
This is then stored in a zip lock bag and hung on a pegboard with all my other jigs hung on pegboard hooks sorted by jig weight and hook size.
Both storage methods make it easier to find jigs and keep track of what to buy when low.
Tip: to store crankbaits and avoid the tangle of treble hooks as well as the inevitable finger
hook sets, I cut the foam into small flat blocks, cut a slit halfway from one side, slide the hook shank to the middle of the slit and push the hooks points into the foam - one block per hook.