It helps with interpreting the estimate of the intercept as the observation where all the Xs are zero will be in the 'middle ' of the data so the intercept is the mean response for a 'typical' person; it is therefore likely to be an interpolation and not an extrapolation. For example if you are modelling income as a response of age, then not centering say as Age-50, the intercept will give the mean income of a new born baby. It does not affect the estimates of the un -standardized regression coefficients. In complex models, centering can also help estimation. I usually think quite hard about centering predictors and using appropriate units of measurement, such as thousands of dollars not dollars, all with the aim of making the estimates more easily interpretable and meaningful for the reader

Another advantage of centering at meaningful values, is that in models that include interactions with another variable, the regression coefficient of that other variable can be interpreted in a more appropriate manner. It is the effect of that variable when the original variable is at the value at which is centered. Otherwise it is the effect at which the original variable has a value of zero, which in many cases, does not make sense or is not of interest.

Also, centering of predictor variables will help minimize the problem of multicollinearity if power terms are included in the model in order to examine non-linear effects, or if product terms are included to examine possible interaction.