An anticipatory illocution is an illocutionary act that has the direct illocutionary force of a question about the conditions necessary for the appropriateness of some other illocutionary act. The anticipatory illocution thus has the indirect illocutionary force of the latter.
Would you like some more coffee?
This illocutionary act has the direct force of a question about a condition for the appropriateness of offering coffee. However, the speaker believes that if the addressee would like some coffee, then an offer of coffee will be accepted. Thus, the question has the indirect force of an offer of coffee.