In the course of performing speech acts we ordinarily communicate with each other. The content of communication may be identical, or almost identical, with the content intended to be communicated.
However, the meaning of the linguistic means used (if ever there are linguistic means, for at least some so-called "speech acts" can be performed non-verbally) may also be different from the content intended to be communicated. One may, in appropriate circumstances, request Peter to do the dishes by just saying, "Peter ...!", or one can promise to do the dishes by saying, "Me!" One common way of performing speech acts is to use an expression which indicates one speech act, and indeed performs this act, but also performs a further speech act, which is indirect. One may, for instance, say, "Peter, can you open the window?", thereby asking Peter whether he will be able to open the window, but also requesting that he does so. Since the request is performed indirectly, by means of (directly) performing a question, it counts as an indirect speech act.
Indirect speech acts are commonly used to reject proposals and to make requests. For example, a speaker asks, "Would you like to meet me for coffee?" and another replies, "I have class." The second speaker used an indirect speech act to reject the proposal. This is indirect because the literal meaning of "I have class" does not entail any sort of rejection.