You can save those items on your retainers for future classes or turn them in for Grand Company seals.

AF is Artifact gear, it is the gear you get from doing the Job Quests to look like classic FF jobs.

Like I said, the only stuff you can store in there is Artifact gear, Seasonal events, and achievement items. So if you didn't get it from a seasonal event like holidays (except for the current swimsuits, that will be stored later), or from getting an achievement like the golden tools, you likely are not able to store it.