The comment posted by the OP to the question (basically stating that the targetSDK doesn't affect the compiling of an app) is entirely wrong! Sorry to be blunt.
In short, here is the purpose to declaring a different targetSDK from the minSDK: It means you are using features from a higher level SDK than your minimum, but you have ensured backwards compatibility. In other words, imagine that you want to use a feature that was only recently introduced, but that isn't critical to your application. You would then set the targetSDK to the version where this new feature was introduced and the minimum to something lower so that everyone could still use your app.
To give an example, let's say you're writing an app that makes extensive use of gesture detection. However, every command that can be recognised by a gesture can also be done by a button or from the menu. In this case, gestures are a 'cool extra' but aren't required. Therefore you would set the target sdk to 7 ("Eclair" when the GestureDetection library was introduced), and the minimumSDK to level 3 ("Cupcake") so that even people with really old phones could use your app. All you'd have to do is make sure that your app checked the version of Android it was running on before trying to use the gesture library, to avoid trying to use it if it didn't exist. (Admittedly this is a dated example since hardly anyone still has a v1.5 phone, but there was a time when maintaining compatibility with v1.5 was really important.)
To give another example, you could use this if you wanted to use a feature from Gingerbread or Honeycomb. Some people will get the updates soon, but many others, particularly with older hardware, might stay stuck with Eclair until they buy a new device. This would let you use some of the cool new features, but without excluding part of your possible market.
There is a really good article from the Android developer's blog about how to use this feature, and in particular, how to design the "check the feature exists before using it" code I mentioned above.
To the OP: I've written this mainly for the benefit of anyone who happens to stumble upon this question in the future, as I realise your question was asked a long time ago.