Think of modal as relating to some "mode," or form. A modal verb is a helper that gives additional information about the verb that follows it, and includes such words as "can," "will," "should," and "may," among others.
The English word modal has long been used as a term in logic and statistics, such as "modal values." Toward the end of that century, the term was used in music, suggesting a use of harmonies and melodies based on other than the standard major and minor scales, in a style found in medieval liturgical music. Modal logic, in philosophy, is a supposition or conclusion based on the ideas of probability and necessity rather than concrete fact.