I'm a user of an iPhone 4 with iOS 7.1.2.
When I want download an app, it tells me it need to update to iOS 8.4, but it's not supported for the iPhone 4!
Is this only a requirement for specific apps or it is a bug?
If you open the App Store page for an app and scroll to the bottom, there's a section titled "Compatibility" that will tell you what the minimum version of iOS is that the app requires.
(This is not a screenshot of the OP's problem app, but rather The Infinite Arcade, which was the first app I saw.)
Apps which require features not available in older iOS versions can not be downloaded on these older versions. The minimum OS requirement is listed in the description of the app in the store.