The smallest building blocks of meaning in a language are called morphemes. Walk, for example, the basic form of the verb, is a morpheme. We can’t break it down any further in terms of meaning. Wal, for example, doesn’t mean anything in Modern English, and nor does alk. The basic form, walk, is what you’d look up in a dictionary, and it’s used when we say I walk, you walk, we walk, and they walk, and also when there’s no particular person attached to the verb, as in He prefers to walk. When we’re talking about someone other than you and me or you and us or several other people, we add -s to the basic form to produce he walks and she walks.
If we add –ed we can create the past tense, they walked. That ending also forms the past participle that allows us to say things like we have walked. Finally, we can add –ing and get walking, and that allows us to make constructions like we were walking. It also means we can say things like Walking is good for your health.
So walk can occur in four different forms. Because it can stand on its own it’s called a free morpheme. It contrasts with the morphemes -s, -ed and –ing which are of no use on their own. To make any sense they have to be tied, or bound, to a free morpheme, and so they’re known as bound morphemes.
Now, take a word like recalculation. That happens to be a noun, but at the heart of it there’s the verb calculate. We can’t break that down any further in terms of meaning, so we can conclude that calculate is a morpheme, and, because it makes sense on its own, it’s a free morpheme. But we can create a noun from it by dropping the –e and adding –ation to give us calculation. -ation cannot be further broken down in terms of meaning, so we can conclude that it, too, is a morpheme, and, because it cannot stand alone, it’s a bound morpheme. If the process of calculation happens more than once we can place re- , another bound morpheme, in front and get recalculation.
A final note on bound morphemes. The bound morphemes -s, -ed and -ing can be added to a verb to show how we want the verb to be understood, but they don’t change its basic meaning. They’re called suffixes because they come at the end of the verb, and because they merely modify the verb, they’re called inflectional suffixes. They contrast with a morpheme like –ation, which creates a new kind of word, a noun. Because they allow us to derive one word from another, suffixes like that are called derivational suffixes. When bound morphemes occur at the beginning of a word, like re-, they’re called derivational prefixes.