Sebastian Sauer has a tutorial for us:
A residual is defined as
ri=yi−Xi^βri=yi−Xiβ^.
That is, a residual is a tangible thing in the sense that it describes observables (cf. Gelman 2021, chap. 11.3, p. 161). That is, the residuals are the difference between observed and predicted values.
Read on for the concept of error terms and how we might plot them.