From
http://www.revenue.ie/en/business/paye/guide/employers-guide-paye-tax-year.html#section2
"2. Week 53, fortnight 27, etc
"Week 53" occurs when there are fifty-three weekly pay days in the year. This happens when a pay day falls on 31 December or, in a leap year, on 30 or 31 December. The employer should set tax credits and the standard rate cut-off point against that payment on a non-cumulative basis (week 1/month 1 basis) in accordance with the following table:
Pay day falling on 31 December (or in a leap year on 30 or 31 December):
If the number of pay days in the tax year is: Then tax credits and the standard rate cut-off point to be set against payment is:
53 Weekly As for week 1 basis ( paragraph 2 - Employee Pay Day – Calculating Tax Due)
27 Fortnightly As for week 1 basis ( paragraph 3 - Employee Pay Day – Calculating Tax Due)
14 Four-weekly As for week 1 basis (paragraph 4 Employee Pay Day – Calculating Tax Due)
As a result, the employee will get the benefit of more than the year's total tax credits and standard rate cut-off point.
If the emergency basis applies, the tax credits and standard rate cut-off point, if any, and the rate of tax deduction will depend on the number of calendar weeks or months since the emergency basis first applied, within the tax year, to the employee's pay (see Calculation of tax under the PAYE System paragraphs 8 - 9)."
So when a week 53 applies, the employee actually does the get benefit of an extra week tax credits and cut off point. This should only happen once every few years.