In philosophy, the notion of intentionality has nothing to do with intentions or intending to do or not to do something. Instead, it has to do with the power of the mind and the mind's ability to be about something in the real world.
According to philosophers, mental images and beliefs are always about something while physical objects are not. I can, for example, have thoughts about a dog or about a pumpkin. But neither the dog nor the pumpkin is about anything. Therefore, my ideas about these things have intentionality while the things themselves do not.
This idea of "aboutness" is called "intentionality" because of the Latin word intentio which was used to mean something like the word "concept."
Intentionality, then, is the power of the mind to have concepts. It is the mind's ability to think about things, to hate things or to love things or to want things. In each case, the mind has the ability to create a concept of the thing. That ability is intentionality.