Microsoft account is the new name for what used to be called a Windows Live ID. Your Microsoft account is the combination of an email address and a password that you use to sign in to services like Hotmail, OneDrive, Windows Phone, Xbox LIVE, or Outlook.com.
If you use an email address and password to sign in to these or other services, you already have a Microsoft account - but you can also sign up for a new one here, or using your phone.
Over time, all Microsoft services will be switching from the old name to the new one. You might continue to see mentions of Windows Live ID instead of Microsoft account for a while - for example, on xbox.com or windowsphone.com - but the names mean the same thing, and the services will be updated soon.
Note: You can also use a Microsoft account to sign in to any PC running Windows 8 or newer.