Plates from Eire used to be pretty much the same as UK plates, in other words black plates with white or silver letters. When we went to reflective plates Ireland did as well but using a red rear plate instead of yellow. They also used letters Britain didn't such as I Q U & Z. More recently they've adopted the current style with the year followed by a locale followed by a number. So D would be Dublin and MH is Monaghan. Probably more logical than the British system but then they have far less vehicles us.
The Irish got a bit superstitious about 2013 and were worried that they wouldn't sell many new cars so instead of having 13 on the numberplate, they split the registration to depict the two halves of the year and used 131 for the first half and 132 for the second half.