Edmund Husserl is a philosopher who focused on phenomenology; he was responsible for popularizing novel concepts such as intentionality, noesis, and noema. Let's review these ideas and then reflect on the questions to get you started on this assignment.
First, let's define the terms. For Husserl, intentionality refers to mental acts such as perceiving, judging, and remembering. It is also the act of experiencing beauty and connecting with others. Intention directs the mind in a particular way of thought, identification, or action. Intention, then, is a broad category for Husserl.
Husserl also speaks of noesis and noema, the two elements of intentionality. Noesis refers to mind-acts, including thinking but also attitudes and feelings. According to Husserl, noesis is what is real. Noema refers to the object that is the recipient of the mental act. It has being but is—in a sense—“unreal” and dependent on the noesis. Husserl might call a flower and the words we often use to describe it —like “beautiful” or “fragrant”—a noema. The noesis would be our perception and characterization of the flower or, more specifically, our thoughts and feelings about it.
We can see, then, why Husserl is so focused on the noesis-noema structure, for it comprises both perception and the perceived in one contained unit. As such we can never completely know the world outside of our limited, individual awarenesses. There will always be something lacking in our thought and perception. So intention is not completely adequate for understanding the extra-mental world. You cannot, for instance, notice or understand every single detail about that flower. Something will always escape you.