Back Boiler/Solid Fuel Stove

New to Ireland, and new to the concept of back boilers. We currently have a back boiler with open fireplace, as well as oil fired central heating. The back boiler requires a pump for operation. I don't quite get the point, as I thought it was to use as a backup.

I'm looking for a system that will keep us toasty and in hot water in the event of a power failure. We'd put in a stove (Stanley Ashling, so I can cook on it) but we're not sure about the back boiler idea. What will work in a rural area with occasional power outages?

Open Back boilers are very inefficient and were very common heating appliances in the 80s/90s. If you fit a stove/range with a boiler incorporated this will be far more efficient once it has a suitable boiler output to satisfy your heating needs.
If you link this appliance up to an oil/gas fired installation take care to install an unrestricted 25mm diameter copper pipe primary circuit that will act as a heat leak (hot water cylinder + small radiator) in case a power cut occurs.
Due care will have to undertaken to install this system as many plumbers cannot install dual heating systems properly leading to expensive heating remedial works.
In my opinion stoves with boilers incorporated as far more efficient than their cooker counterparts.

Thanks for that advice. We will take it on board, for sure.

Am I understanding correctly that there should still be a pump on the system and that the heat leak just prevents issues during a power cut?

There will be pump on the heating circuit from the stove. This circuit will be linked to the heating circuit from other heat source. The primay circuit will work on convectional gravity circulation to the cylinder/heat leak radiator therefore not needing forced circulation aided by a pump. Therefore if there is a power cut/failure this circuit will work safely.