Why is it important to find out who the speaker/author is in a poem?
This is a good question. There are two issues here - the author and the speaker of the poem. Let me deal with the author first and then the speaker.
It is important to know something about the author to appreciate a literary work in greater detail. If you know something about the culture of the author, then you might gain some cultural insights. For example, to know that Homer's Iliad was written in a culture that prizes courage, cunning, and glory is very helpful. The more you know of the historical and cultural context, the more you will be able to understand a poem.
Second, the speak of the poem does not have to be the author's voice. The author can uses different perspective. In literary circles, this is called focalization. So, an observant reader will always seek to determine from whose perspective is the story being told.
It is important to remember that author does not equal speaker.
The author is literally the person who wrote the poem, and is not necessarily the voice of the poem; that is the speaker of the poem.
In the poem "Madam and Her Madam" by Langston Hughes, Hughes is the author, he wrote the poem. The speaker of the poem is a woman, presumably a black woman, who works for a white woman. This is a clear cut difference, Hughes is a man and Alberta in the poem is a woman. The speaker here allows the reader insight to her life and situations that Hughes himself hadn't experienced.