The default behavior of Abnormal is to edit the normals of the vertices. We aren't actually editing the vertex's normal (a single vertex normal), we are editing the loop normals of the faces connected to the vertex.
A loop can be thought of as the corner of a face where it connects to the vertex. This corner is what controls the shading of our object and is what we are editing.
When we select a vertex and change it's normals we are changing the loop normal of every face corner connect to that vertex. With Edit Individual Loop Normals turned off we have no control over the individual face corners normal.
By turning on Edit Individual Loop Normals we can control each face corners loop separately to create hard shading breaks in our model if desired. This referred to as "Split Normals"
This is the difference between Flat Shading and Smooth Shading. Flat Shading the loop normals of each vertex are all aligned into a single vector creating a smooth transition. Flat Shading every loop normal can be a different vector on the same vertex.