It is a code file automatically generated by your designer to hold the form's layout information that was created using the Visual Studio IDE. Previous versions of Visual Studio stored all of the information contained in the .designer.cs file in the main code file but the split it out due to user feedback.
Basically it means the ".designer.cs" file is for setting up the form where you can drag buttons around, add panels, resize the form, etc. Whenever you make a change visually with the development environment the changes are stored in .designer.cs.
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