The subject of a poem is the idea or thing that the poem concerns or represents. Looking for the poem's subject is natural. Almost all poetry has messages to deliver — lots of them, profound and diverse as stars. But these messages are sometimes hidden, and you have to read attentively to make them out.
You might think that the subject is what a poem is about. But that's not exactly right, because it implies that what a poem says is all there is to a poem. If that were so, why would people go to the trouble of writing poetry? Instead, people go to the trouble because poems sound a certain way, are built in certain shapes, and have certain beauties in sound and meaning — all of which accompanies the meaning and goes beyond it.
Not all poems have a single subject. Some poems have many subjects, and some have subjects that aren't clear. Sometimes a poem's subject is simply itself — the words in it and their relationships to one another. The point is to be alert for the subject (or subjects) of any poem as you read.