The red banner at the top of the screen tells you which Great Power was victorious and displays a list of the forces engaged in the battle. The location of the battle is displayed by an icon on the map.
You may cycle either using the two arrow buttons, or by selecting a different battle icon on the map. The icon for the selected battle flashes. The icon is color-coded according to the results of the battle. Red means your forces were defeated. Green means you won a victory. White means the battle did not involve your fleets or armies.