To expand on what Deepanshu said, you should understand that there are several different dimensions at play when it comes to building and testing an app:
- Minimum API level: this is the minimum API on which your app can run. If you specify a min api of 16, users with ICS or earlier installed won't be able to install the app. You should probably set this to the lowest number you're able to, while still getting the APIs you want. Note that if you use APIs in the Support Library (as you should) and specifically the appcompat library, you should be able to make your app compatible with more versions than you would otherwise be able to, since appcompat will replicate similar behavior using whatever APIs are available on the user's device. You can see information on the impact of the min api level choice in the dashboard linked above, or in the new project wizard in Studio.
- Target API level: this is the actual platform you're compiling against, and what I assume you're asking about. Note that, unless you're calling specific APIs added at this API level, and not provided by appcompat, your app should be backward compatible with previous releases. This is why we recommend always using the latest platform as the Target API: if you're using the latest, you can always (conditionally) limit the API calls you make such that you get the benefits of the newer platform when running on newer devices, while maintaining compatibility with previous devices.
- System Image/Emulator API level: these are the emulated devices you'll actually test on, and what Deepanshu was mentioning in his second comment above. The system images for an api level are completely separate from the platform for that api level; you don't need one to use the other. If you want to test your app on a certain device, all you need to do is create a new device in the AVD manager, and on the system image selection page click "Show downloadable system images." Then from right there you can download whatever system images you like, create an AVD, and run your app on that device. You should probably test against API Levels down to the one you specified as the Minimum API level for your app.
For more information:
"Supporting Different Platform Versions": http://developer.android.com/training/basics/supporting-devices/platforms.html
Support Library: http://developer.android.com/tools/support-library/index.html
"What is API Level": http://developer.android.com/guide/topics/manifest/uses-sdk-element.html#ApiLevels