First it is important to understand what a sphere(s) of influence means. It is an outside influence from another country (or more than one) that claims exclusive rights to a region of a different country.
In Persia, Russia and the British Empire established spheres of influence through the Anglo-Russian Convention of 1907. Neither were interested in Persia itself, but where it was strategically located.
The British Empire wanted to protect India from Russian expansion in the area, and Persia was close by.
The Russians were expanding in that area and seizing parts of Persia.
They made an agreement to control different spheres of influence in Persia (Britain the east and Russia the north).