The min sdk version is the earliest release of the Android SDK that your application can run on. Usually this is because of a problem with the earlier APIs, lacking functionality, or some other behavioural issue.
The target sdk version is the version your application was targeted to run on. Ideally, this is because of some sort of optimal run conditions. If you were to “make your app for version 19”, this is where that would be specified. It may run on earlier or later releases, but this is what you were aiming for. This is mostly to indicate how current your application is for use in the marketplace, etc.
The compile sdk version is the version of android your IDE (or other means of compiling I suppose) uses to make your app when you publish a .apk file. This is useful for testing your application as it is a common need to compile your app as you develop it. As this will be the version to compile to an APK, it will naturally be the version of your release. Likewise, it is advisable to have this match your target sdk version.