How to correct for autocorrelation in Excel

I do not understand how to correct for autocorrelation. One website easily describes how to do it in excel however I could not find any sources to verify this:

This is the site that explains how to correct, however my question is after you lag the dependent variables, why does it now become the new independent variable?
More importantly, it suggest that when I re-run the regression (simultaneously rerunning the Durbin-Watson test) that I will keep the dependent variable the same (Price), and run it against the new independent variable "Lag1Price".

I do not understand why I run the new lagged independent variable against the dependent variable and not against the "time" as I did in the initial regression.