Morphology is all about the meaningful parts of words that go together. These are called morphemes.
A typical way that morphology is shown, is through affixes, small units of meaning that attach to a word (or technically around a stem, which may or may not be a word in itself). The most common types of affix are prefixes that go at the beginning, and suffixes which go at the end, though some languages have infixes which go inside a word or circumfixes which go around a word.
See the entry for affix for examples of these.