we started to develope an application with swift for iOS.
when we started it latest version was developer target 9.3.
now there is developer target 10 available. Can I install application that created with developer target 9.3 on iOS 10 ?
['https://Stackoverflow.com/questions/40625869', 'https://Stackoverflow.com', 'https://Stackoverflow.com/users/4433550/']
In short - YES. You won't be able to do the opposite - install targeted as iOS 10 app to device, running with iOS 9.3

EDITED

So, your purposes, I think, maintain as small version, as possible. If you maintain 9.3 version, for example, your app will be available for iPhone 4s, which is not updates to iOS 10. With this ver you will cover more users
**Deployment Target** is the **minimum required iOS version you application needs to run**.

You can build an application with SDK 10 that runs under iOS 9. But then you have to take care to not use any function or method that is not available on iOS 9. 

Also Always check to see if you are using deprecated APIs; though still available, deprecated APIs are not guaranteed to be available in the future.