Blender has several modes. This page explains basic.
As explanation in the Window, left image shows non selected, right image shows selected object. At this time, these are in the Object mode.
Press "Tab key" while the object are selected in the object mode. After that, you can see like this.

This mode is called Edit Mode. Comparing the object mode, this mode shows yellow dot. This is called "Vertex" which consists of mesh. And the line between vertecies is called "Edge". This situation that the vertex is yellow means that the object is in the edit mode and vertecies are selected.
I explain in the Editting Mesh, but if you press "A key" in the situation, the vertecies are change to following image.

The vertecies turned to purple. This means that the vertecies are not selected. "A Key" make all vertecies in the screen selected or non selected.
Changing those mode can be controlled by "Tab Key", but on the other hand, it can be done from the menu in the header.
