"the Russo-Turkish affair"
Russo-Turkish War
Public DomainRusso-Turkish War - Credit: Pavel Kovalevsky

This refers to the Russo-Turkish War of 1877-1878.  The war began with rebellions by Bosnia and Herzegovina and Bulgaria against Turkish rule.  The Russians came to their aid, attacking through Bulgaria and advancing into Turkey. 

Concerned by the growing level of Russian control in the Balkans, the British put pressure on the Russians to accept a truce offered by the Ottoman Empire in 1878.  Under the treaty of San Stefano, the Ottoman Empire agreed to recognise the independence of Romania, Serbia, Montenegro and Bulgaria.