I did not read this text, however I can probably guess what the author's claim was to help me write a explanation. Basically, this quote means that even though Armstrong just took a simple step, all the work and effort it took to successfully go to the moon made it so much worthwhile to be able to experience this. Going to the moon allowed so much new information and humans began to realize more about space. Basically another way of putting this quote could be small things can make big differences.
Hope this helped!!! Sorry if it didn't! Good luck on the assignment! I bet you will do great!!!! :)