Welcome to the Mac.
Your Mac has a program called "Mail", which is an email client — it enables you to have your email delivered down to your computer, rather than having to go online (like to Gmail or Hotmail) to check it.
However, it seems you're also asking if Apple has its own email service, which it does. However, Apple's service (called MobileMe) is more than just email — it's a service that gives you 20GB of online storage, a website, push syncing of information between devices (like an iPhone), and many other things. Due to the vast amount of stuff included in MobileMe, it's a service that has an annual fee of $99.
Note that, if all you need is email (and not all the extra goodies that MobileMe comes with) sticking with Gmail is just fine.