The poem is addressed to somebody who the speaker loves. For the sake of clarity, we shall assume for the moment that the speaker is a woman and that the addressee is a man. The speaker in the poem is telling the man that there is a place in her heart for him or perhaps that there is a way to her heart for him.

The human heart is comprised of four chambers, which are called the right atrium, the left atrium, the right ventricle, and the left ventricle. Between these chambers, there are valves which control the circulation of the blood between the chambers.

In the poem, the speaker refers to "Four Simple Chambers" and "A thousand Complicated Doors." The "Chambers" and "Doors" are here intended as puns (or play on words). This is because they at once connote the biological components of the human heart, whereby the doors represent the valves and also literal chambers (meaning rooms) and doors.

The question I think your professor is asking you to grapple with is why the poet would use these two words, "Chambers" and "Doors," to mean two different things at once. On the one hand, the image of rooms and doors connotes a physical space, and on the other hand, the chambers and doors (if we take doors to represent valves) represent a human heart.

Perhaps the speaker deliberately creates these two contrasting, simultaneous images to suggest that her heart, in a figurative sense, is a complicated, labyrinthine place. The implication might be that her emotions are complicated or that there are lots of people who she loves and who have a place in her heart.