A written birth plan helps you communicate your concerns and wishes to your medical practitioner. Discussing your plans for childbirth before you go into labor is essential, and having a written plan in hand can be a huge help.
Never assume your medical practitioner's idea of the perfect birth is similar to your own. Even if your chosen care provider shares your birth philosophy, you should still write down your wishes to prevent misunderstandings.
If you're giving birth in the hospital, you have very little control over which nurse you get, and you get very little time to discuss your birth plans with her. Most nurses want their patients to have a healthy and positive birth, and a written birth plan makes it easier for them to provide you with what you want.
Just writing your plan down won't magically make your birth wishes a reality. Not every option is available in every birth location or with every medical practitioner. Even if the option is available, you still need to advocate for yourself beyond handing your nurse, midwife, or doctor a written birth plan.