The icon looks like a fountain pen. Drawing tools work by using anchor points and paths. You can manipulate these points and paths to create curved lines or straight lines. There is a VisiHow tutorial on "Pen Tool".
After selecting the "Delete Anchor Point Tool", click a line to delete the anchor point
You can manipulate shapes quite dramatically or delete mistakes using this tool. It may be better to create a shape or line in InDesign, instead of copying and pasting one from Illustrator. You may lose some of the quality of your image or design if you use the copy-and-paste technique, since these programs are used for different types of media.
This is a VisiHow tutorial. I've just shown you how to delete anchor points in Adobe InDesign CS6 in Windows 7. If you have any questions or comments, please leave them in the comments section below. Thank you for watching VisiHow!