Morphology is derived from two Greek words, μορφή (= 'morphe'), 'shape', and -ολογία (= 'ologia'), 'study [of]'. In general it means '[the study of] structure, shape or form' of something, [usually a group of things].' It has several specific uses in different subjects, some in the biological sciences and others in mathematics and other subjects.
Users of AWE are most likely to need the sense in linguistics: "The structure, form, or variation in form (including formation, change, and inflection) of a word or words in a language; the branch of linguistics that deals with this" (OED). There are two large divisions of the subject: