It's all about transposing prices into some space that changes more slowly, such that data you can garner from prices provided by someone else at some other point in time can be used to estimate value at some other point in time.
Its effectively an interpolation and extrapolation tool.
Say you have option prices at strikes of 10, 20, 30, 40, etc. And you want the price for a 35 strike option. You could interpolate in price space, or you could transpose the option prices into vols and then interpolate in vol space. The latter works better. Even more obvious, if you need to extrapolate to other prices, then you can take the volatility "smile" from the strikes you have, and attempt to extrapolate this, it will give you a potentially better answer.
Likewise, if you have the option prices from one day, and then you need to calculate them the next day, you can adjust the underlying stock price, expected dividend yield, discounting, and time to maturity while keeping the volatility the same as your previous data point, and it will give you an idea of the option price.
Black Scholes is a model that everybody knows does not work. This is evident by the fact that every option strike has a different implied volatility (despite one of the underlying assumptions of the model being that volatility is constant). What it is though is a very useful function for transforming option prices into another space which allows you to estimate the value of that option given changes to other underlying properties.