Image source: http://www.cosc.brocku.ca/Offerings/3P98/boomerang.jpg
A boomerang is concave so that the curvature in the boomerang helps it return back to you after you throw it.
Image source: http://www.m-b.com/acatalog/stapler.gif
A stapler is concave so that a stack of papers can squeeze between two of the
Image source: http://www.canesgalore.com/images/cane.gif
The handle of a walking cane is concave so that it is easier to hold.