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Reminders is an application included in Mountain Lion, so you have to upgrade OS X in order to use it with the computer.
First, check that your MacBook is supported > http://www.apple.com/osx/specs Then, open the App Store and purchase Mountain Lion. While it's being downloaded, make a backup of your data and check that your apps are compatible > http://www.roaringapps.com
When the download finishes, the OS X installer will show up, so follow the steps to upgrade to Mountain Lion. After upgrading, you will see Reminders in the Dock, so open it and you will be able to sync reminders between the computer and the iPad