1.With Mail open, go to "Preferences" in the top left corner under the "Mail" menu bar.
2.Be sure you are clicked on the "Accounts" tab in the Preferences window.
3.Also, make sure you have selected the correct e-mail account on the left hand column.
4.Halfway down it will allow you to update your password.
5.Once updated, simply close out of the window. Select "Save" to the changes that are made.
Screenshots for reference: