Intentionality refers to the notion that consciousness is always the consciousness of something. The word itself should not be confused with the "ordinary" use of the word intentional, but should rather be taken as playing on the etymological roots of the word. Originally, intention referred to a "stretching out" ("in tension," from Latin intendere), and in this context it refers to consciousness "stretching out" towards its objectIntentionality is often summed up as "aboutness." Whether this something that consciousness is about is in direct perception or in fantasy is inconsequential to the concept of intentionality itself; whatever consciousness is directed at, that is what consciousness is conscious of. This means that the object of consciousness doesn't have to be a physical object apprehended in perception: it can just as well be a fantasy or a memory. Consequently, these "structures" of consciousness, i.e., perception, memory, fantasy, etc., are called intentionalities.
Having a cup of coffee in front of you, for instance, seeing it, feeling it, or even imagining it - these are all filled intentions, and the object is then intuited.