Although you can label selected features manually using the New Text label tool, you cannot automatically label selected features in ArcMap. The steps below show how to create an annotation layer containing labels of the selected features.
Right-click the layer and select Label Features
Select the features you want to label.
Convert the labels to Annotation
Right-click the layer in the ArcMap table of contents and click Convert Labels to Annotation.
Click the 'Features Currently Selected' button.
Click the 'In the Map' button from the Annotation Storage options.