The Mac has supported multiple displays since system 4.5 (circa 1987).
Mirroring is available, but that is not what you want. Choose Extended Desktop, and the area from the second screen will be added to an edge of your existing screen, extending it in the direction you specify. Then place additional Windows on either screen, or even split across screens.
If you are using Mountain Lion or earlier, this article describes the features available and how to use them:
OS X: How to use multiple displays with your Mac in Mountain Lion and earlier - Apple Support
Regardless of what Mac OS X version you are running, you should become familiar with those features, especially under the Extended Desktop section. Later versions of Mac OS X add some more complicated options in addition to all those features.
The main complicating feature is taken directly from iOS, the land of tiny screens and one-at-a-time processing. It is called "Displays have Separate Spaces" and is only helpful if you want to have several different Applications assigned to several different displays. Otherwise it is a nuisance and needs to be turned OFF.
This is accomplished completely counter-intuitively in Mission Control:
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