Gamma risk and delta being a linear approximation

Apparently when we use delta, we are using a linear relationship to estimate a non-linear change which creates an estimation error and that gamma approximates this estimation error.

I don’t entirely understand this statement. My guess is this has something to do with the fact that we are using calculus here.

Okay I haven’t done calculus in years but…I think when you take a derivative of a function you effectively get a new function that is a tangent to the original function. In this case you will get a tangent line to the options price vs stock price curve.

Hmmm I’m confused. Can someone help?

Thanks