"She eats a banana."
Translation:Itheann sí banana.
Not sure what your question was. But an gives a sense of definitiveness to the banana. It's not just any banana she ate, she had that specific banana. There would likely be a prior understanding between the speaker and the listener as to what banana she's eating.
Simply put, Irish an is akin to the Englisb definitive article the. Without it, you may insert the word a in an English translation, or leave it off.