These arise where a firm is not owned outright by another firm – its “parent” company.
Say for example a predator buys 80% of another firm’s voting shares. It now has control of the entire business since it can outvote other shareholders. When it produces its accounts which combine the two firms together this control is reflected by adding both balance sheets together. However somewhere in those same accounts the part of the target firm that is not owned must be disclosed – this is called a minority interest.