In the ArcGIS for Desktop documentation the About feature templates page says (with my bolding):
Creating features is accomplished through the use of feature
templates. Feature templates define all the information required to
create a feature: the layer where a feature will be stored, the
attributes a feature is created with, and the default tool used to
create that feature.
It is not possible to create a feature template until there is a layer in the map, and to create a layer it needs to have a data source.
Consequently, you need to first create a feature class in the Catalog window (or via the Create Feature Class tool), then add it to your map so that there is a layer with it as the source. A feature template will then be automatically created if that layer is turned on when you start editing.