Deanna R. answered 04/12/19
Professional Digital and Traditional Artist
They want you to focus on the shift from one part of an object to another. When you're told to "push your values" it means that you aren't showing enough confidence in your shading. Do a few 20 minute or less sketches of simple objects. Draw in the darkest shadows as dark as you can, even if they look light, then blend your shadow to the light area and make the lightest parts white.
You'll notice how much more it pops, even if it doesn't seem quite "accurate." After you've done a few studies like this, try drawing something you want again, but with the confidence you had of those 20 minute sketches. The biggest problem artists have when it comes to values is their fear of themselves.