View->Show Bounding Box.
It's not over part of a path, it's over the entire path (or mutiple paths, if the selection contains them). In the screenshot, each gear tooth was a separate path.
The bounding box does surround the whole selection. The other sprocket teeth are the result of the live Transform Effect that is applied to the selection.
Search for and read about Transform Effect in the documentation.
The other two posters are absolutely correct.
But you have two choices to do what you want as far as I know since your path is not an effect as mine was.
You can use the scissor tool to cut the segment you want to be able to select. I assume you want to move it or rotate it or perhaps resize it or a combination of those.
If you need the original path to remain intact you can take the lasso tool and select that segment of the path and do a copy and then a paste in front and you will have a copy of that segment sitting on top of the original segment which will still be part of the original path.
If you intend to alter the segment and then rejoin it to the original path then use the scissor tool approach.
In case you are used to Photoshop which does give you the transformation box (Ctrl + T) only around the selected points and not the entire path, the alternative in Illustrator is to use the scale and rotate tools which Photoshop is missing. You use these tools by first clicking on the spot that defines the center of scale/rotation and then click + drag on any other place to transform. Farther away you click + drag from the center, finer the control. You can hold Shift to constrain the transformation - drag diagonally for proportional scale.