Not quite store - simply, whatever you don't use in the previous month, half of that will be added to your regular allowance every month.
For example, if your allowance in month 1 is 1TB and you use 500GB, you would get half of that (250GB) added to month 2's regular allowance, making for a total of 1.25TB. If you again only use 500GB of this, in month 3 you would have 1.375TB and so on.
In other words, only half rolls over and you can't "store" it, but you can continually increase your allowance to up to 2 times your normal quota, if you don't use very much.
In other words, it helps to smooth out the peaks and troughs of regular use (e.g. holidays, visitors, large OS/game updates).
I for one will gain a lot from this and the recent 50GB addon, as instead of having a fixed 150GB that, if exceeded, would immediately cost £10 for 50GB that are then lost at the end of the month, I now have at least 200GB, which if I exceed I have to pay £10 but get to keep that until I next need it, and if I use less I can save up for next month.
I was on the brink of considering cancelling AAISP and switching to "unlimited" but this may just have saved them