|Photo Source: Defence Research and Development Canada|
Despite what the movies would lead you to believe, it's pretty much impossible to see the shockwaves of an explosion most of time.
Did you hear that qualifier? Most of the time. That means that sometimes, you can! With your own, pathetic, human eye! Isn't that exciting?!?!!
The folks at Fuck Yeah Fluid Dynamics do a much better job of explaining it than me, but my no-science-classes-beyond-grade-11-except-the-nutrition-class-I-took-so-I-could-graduate-university understanding is this: sometimes in an explosion, the conditions create a sudden, sharp change in density in the air around the explosion, changing how the light hits that part of the air and thus making it visible.
Of course, the downside of this is that you will not be able to see this cool shockwave effect if you are dramatically walking away from the explosion, in slow motion, without looking back.