The cap refers to the maximum possible amount of money that can be deducted from the Leap Card on any given day (or week if you use it often enough over a full week), the same as with the Oyster Card in London.

You swipe the Leap Card against the validator if your fare is above 13 stages (or if you know you're going to be travelling enough to activate the cap because you cannot be charged more than the cap for a day).

The personalised Leap Card will have your photo on it and consequently is not valid if anyone else uses it.

Note that only PSO services operated by Dublin Bus count towards the cap. Commercial services operated by Dublin Bus either do not count or only a certain amount of the fare counts i.e. Xpresso, Nitelink etc. I think there is some sort of cap for commuter services in the greater Dublin area, but I've never checked.

As far as I know it's planned to introduce capping on Cork city services as well once the Leap Card is rolled out there in the next few weeks.

If the Oyster Card is anything to go by, there will be a small allowance if you're out of travel credit.