What is app.aps file in Visual C++?

It's a generated file for designer efficiency, you can ignore it in source control:

File created by Microsoft Visual C++, a software development application; stores the binary representation of a resource included with the project; enables the application to load resources more quickly.

http://fileinfo.com/extension/aps

APS files are the binary versions of resource files. As resource editor does not directly read the .rc and resource.h files, the resource compiler turns them into the APS file.

Reference - Files Affected by Resource Editing