Offset means that any tax paid in US is deducted from tax bill in ireland (you calculate the tax bill in US and pay taxes accordingly in the US. You then have to calculate the tax bill in Ireand under irish law (see above). The tax paid in US can be deducted from any tax paid in Ireland.
Not sure how the situation is in the US but lets assume the tax due is USD 2000 or say 1500 Euro.
In Ireland
(All figures converted to Euro)
Rental Income .............................................15,000
Less interest on Mortgage ....................8000
.......Wear & Tear Furniture/Fittings etc ..1000
.......Other Expenses............................1000
Total Expenses ............................................10,000
Total Profit ...................................................5,000
Tax @ 41% ...................................................2,050
Less tax paid in US .........................................1,500
Tax due in Ireland .............................................450