These introductory youtube videos are helpful in understanding how/what we are measuring to work out the efficiency of algorithms.
Big O Notation (The internet vs pigeons) https://www.youtube.com/watch?v=v4cd1O4zkGw
Big O Notation (Story behind it) https://www.youtube.com/watch?v=Q_1M2JaijjQ
Big O Notation (What is it?) https://www.youtube.com/watch?v=__vX2sjlpXU
Combinatorial Explosions
Exponential Growth: How Folding Paper Can Get You to the Moon (Youtube) https://youtu.be/AmFMJC45f1Q
Combinatorial Explosions: How many ways can you arrange a deck of cards? (Youtube) https://youtu.be/uNS1QvDzCVw
Check out the Travelling Salesman problem - the number of tours for a n=3038 city TSP is astoundingly immense http://www.math.uwaterloo.ca/tsp/problem/pcb3cnt.html Which is a Combinatorial Explosion!!!!