A back boiler is a form of heat only boiler. The boiler itself is located in a chimney breast with a gas fire on the front. The boiler will work with a hot water cylinder.
It is no longer possible to replace a back boiler in the chimney breast, as manufacturers have not yet been unable to meet new efficiency standards for this type of boiler. If you have a back boiler then you can either opt for a new wall hung heat only boiler elsewhere in the house and retain your hot water cylinder or consider a combi boiler and remove the hot water cylinder, providing your hot water pressure is good enough.