Prime has a lot of different bonuses. Essentially with Amazon it's a WYSIWYG. You want to buy something, you buy it, pay for shipping, and it shows up sometime in the near future. Most people view Amazon for its shopping capabilities. It has much more to offer, though many people won't need the extra features. With Prime (Standard ~$100/year) you get the following.
free 2 day shipping on most items.
Some zip codes can have same day delivery
Some areas get Prime Now which is 2 hour delivery
Free Restaurant Delivery
if you are the pre-order kind of person, some items ship with a release date delivery guarantee. IE, you pre-order a game that released December 14. Instead of it shipping on December 14 and getting there a few days later, it'll ship the day before and arrive the day it releases.
Prime Video: Like Netflix. Has originals that you can't watch elsewhere.
Prime Photos: Online storage of all your photos unlimited capacity.
Prime Pantry: online grocery shopping for a low cost delivery
Amazon Elements: Their own product line.
Amazon Dash Button: Press a button, shit shows up 2 days later for commonly used items (Think detergent)
Early Access: 30 minute early access to deals
Kindle Lending Library: Loan out your digital book library to a friend.
Prime Reading: Borrow books from Amazon.
Audible Channels: Get access to Audible for free
Amazon Music: Like iTunes Music or Google Music
Amazon Family discounts: Have a newborn or kid? You can get discounts on common products (Diapers etc...)
That's the list from their "What do I get" page.
Here's what I will say about it all. You'll use the 2 day shipping assuming you buy crap online. Music and video will get used. The rest may or may not get used. Those are nice, but there tends to be better or concurrent options which you'd also use.
For instance. Amazon Music is pretty weak compared to the competition. With Google Music, I pay $15 a month and myself and 5 people can have full access to Google's music. If it's just you, it's $10 a month. Unlimited streaming. The selection blows away Amazon Music and is comparable to Apple's Music service.
Amazon Video is ok. I use it to watch some of the limited content (Man in the High Castle) but use Netflix for anything else. The content on Netflix is far better to choose from.
Photo Storage: I use Google Storage. It's easy to use, features in it are great, and it's free. So if I decided to not renew my Prime membership I'm not splitting my photos between service providers because Amazon included it as part of their prime membership.
It really comes down to what do you want to pay for that will be better elsewhere, or are you content just getting the package deal through Amazon that isn't quite as good as the competition.