First of all, you are free to specify practically any linear or non-linear model you want for your data. Sometimes there is a theoretical basis for the model. Often, there is not. As such, empirical models often do not have a completely physical interpretation like their theoretical counterparts. That is to say, each term or parameter has a role, but not necessarily represent a direct physical attribute.
The constant term in a polynomial expansion that is used as the linear predictor in regression is an empirical model. The intercept could be interpreted as the y-intercept at x=0, but that is not its only purpose or use. It is the mean response at the origin, which is useful if your predictors are centered. Centering is not based on a theoretical model. It is based on the performance of the regression method. It improves the power of the hypothesis tests of the parameters by reducing the correlation of the parameter estimates when terms above the first order are included for example.
Finally, there might be other contributions to the response y even when the predictors are all at zero leading to a non-zero intercept.