Making a statement may be the paradigmatic use of language, but there are all sorts of other things we can do with words. We can make requests, ask questions, give orders, make promises, give thanks, offer apologies, and so on. Moreover, almost any speech act is really the performance of several acts at once, distinguished by different aspects of the speaker's intention: there is the act of saying something, what one does in saying it, such as requesting or promising, and how one is trying to affect one's audience.
The theory of speech acts is partly taxonomic and partly explanatory. It must systematically classify types of speech acts and the ways in which they can succeed or fail. It must reckon with the fact that the relationship between the words being used and the force of their utterance is often oblique.