Of course this is different than rechargeable batteries, which take considerable time to recharge, trickle out a constant charge over a relatively long period of time, can store a pretty decent amount of energy, but can be only be recharged perhaps several thousand times.
For quite a time now, engineers have been working on Supercapacitors. Ideally, these would combine the positive benefits of capacitors (quick recharge time, high recharge count) and recyclable batteries (high power density, slower controlled discharge rate). Hence the prefix "Super" - they are pretty neat things.
Now comes along a team of researchers working on High Tensile Strength Structural Supercapacitors . It's apparently been tried before with carbon fiber, but this team's new approach holds 3-4 orders of magnitude more charge than previous efforts, comparable now to regular Supercapacitors. And the "high tensile strength" part means they are tough little cookies.