As a beginner, it can sometimes be hard to discern what different terms and phrases mean in QF. I've heard multiple people such as academics and market-makers say things like "calibrate vols" or "calibrate to the market" but I'm not exactly sure what this means.
Focusing mainly on Vanilla American and European Options on equities, I know there are multiple models to price these Options such as Black-Scholes, Local Vol, SVI, etc...
Most of the time, the observed prices of Options you see in the market are quoted from the Black-Scholes model and therefore the "market" implied volatility is from BSM as well. If one were to transform the observed prices and volatilites into a 3D surface (vol surface), we would usually observe skew because the Black-Scholes assumption that all vols are constant along strikes is false.
So when it's said to "calibrate vols" what does that exactly mean? I assume the premise of that is to see whether or not the Options prices or implied vols from Firm XYZ's model line up with the market's quotes and from there underpriced vol would be bought while overpriced vol would be sold.
But when they "calibrate vols to the market", does that mean they input the Market price of an Option into their own model and see whether or not the BSM implied vol from that market price lines up with their (presumably better informed and more correct model) own model's implied vol? Or is it vice versa?