1. Makes you realise if there are any grammatical errors.
2. Shows where there are clumsy sentences (where you stumble reading, you can be sure the reader will also stumble).
3. Gives you a sense of the rhythm of your writing, particularly when it comes to the dialogue.
Rhythm is something we don't often talk about, but it's there in everything we write. I write with a different rhythm to you, and you write with a different rhythm to your friend and so on. Our rhythm is as individual as our fingerprints - it's one of the aspects that makes up our 'voice' as a writer.
People speak with different rhythms, and this is one of the hardest things to get across in dialogue. You have to hear how your characters speak, and then transfer their different speech patterns to the page. If you've got a good ear you'll do it naturally, but other people have to practice - a good starting point is learning to listen.
Try saying both these phrases aloud: "That's enough" and "Enough already"
I bet you said them with a different intonation. They mean the same, but the different words give a different rhythm, which show a different accent, which suggests a different background. Read a Roddy Doyle novel, for example, and the Irish accent rings out clearly through the rhythm of the sentences. Listening and reading out are key in developing this for yourself.