I raced motorcycles then came to the world of cycling. both sports I have played with gearing by dropping a tooth or gaining. I understand the reasons to do so and how it effects the performance, but I have never been into engines or working on stuff myself so I guess I never really thought about how it works. I understand the reason of using a larger or smaller tooth cog or ring. I'm looking for a simple explination on how shifting from one cog to the next size cog, to the next cog, to the next cog makes it easier or harder.

my thoughts are that if you shift into your highest gear on the cassette (Biggest rear cog) the chain is tighter and the smaller the cog the more slack (is that right or do I have it reversed?). regardless if you go to a higher or lower gear, how does that make it easier to pedal?

I'm sure this is very simple, but I dont know the answer. I'm sure once it is explained, it will become very obvious and feel very stupid