The ship is an Admiral class ironclad, most likely to be HMS HOWE 1885, (Rodney 1884 was similar.)
The heavy mast is equipped with a fighting top and rigging to enable auxiliary sails to be raised if necessary
Spike Island is in Cork Harbour and for centuries has been a defensive and defensible point - hence Military use. Nowadays a tourist attraction.
On the very right hand side of the photograph there is a piece of land visible, this is Haulbowline Island. The island was formerly an army supplies base but over the years became a Royal Navy dockyard and drydock. I have a photograph which shows HMS Howe in the drydock, so the Howe was stationed in Cork sometime in the 1890's or there about.
There is a painting called The Evening Gun showing HMS Conqueror in the same anchorage off Queenstown.