Cohomology is one of the major ideas of modern mathematics. Not just an abstruse technical device for proving other abstruse technical facts, it's beginning to see use data analysis as well. Cohomological ideas can be found in surprising places. If you liked this article, you might also like this one, which explains how carrying in digit arithmetic is a cocycle:
http://www.math.wayne.edu/~isaksen/Expository/carrying.pdf