I found the same thing on my online account last Friday and when I rang AIB about it (they don't let you ring the branch directly anymore) they were very closed mouthed about the whole thing but told me that I should expect a letter today, Tuesday, if I hadn't received one already, which I hadn't.
Today came and no letter so as I was in my branch anyway, I asked at the customer service desk and was told that they would find out about it and get back to me, though they were insistent that I had been written to about it.
Anyway, they did get back to me some hours later and their story was this. In 2003, those who signed up for internet and phone banking were promised extra interest on their accounts, and that said interest was either not applied, or calculated incorrectly. The lodgement to my account now is made up of what I should have gotten then, plus a payment as compensation, though they could not tell me how much each was.
Furthermore they told me that as my amount came to less than €10.00, that they were not obliged to send any letter and hadn't, and that this rule applied not to just AIB but all banks and financial instutions.
While I was glad to get the €9.80 I was a bit annoyed that the bank could keep my money for 7 years and then return it without even telling me that they had witheld it in the first place - so I contacted the Financial Regulator's office on this point and they too asked if they could call me back. When they did, they state quite categorically that no rule exists, and where there have been any errors or overcharging or anything of that nature, that every bank is obliged to inform every customer involved either by phone or by letter.
That's all I can add to clear up the mystery for now.