This selection tool is useful if you want to select all faces connecting one another from the selected face.
How to Use
The sphere and the other shape in the following image is in one designer object but they are not connected with each other.
With a face in the sphere selected, if you press the "Connected" button, all the faces in the sphere will be selected but the faces in the other shape won't be selected because the other shape isn't connected with any edges to the sphere.
In the case that a face in the other shape is selected, when you press the "Connected" button all the faces in the other shape will be selected but the faces in the sphere won't be included.