Branding yourself - adding your image, detailed contact info, website links will add to the value of your page. It will get more people to know you better and follow you.
Contact details - the page background gives you the opportunity to add your contact information like web url, email, phone numbers and other details. It helps you get valuable leads for your business/profession where you can mutually benefit.
Inspiration - you can make your background a real creative piece of art. It will surely inspire others to check your profile and read your tweets.