The file extension .C10 is that given to the first part of a WinAce split compressed archive.

A WinAce split compressed archive is a compressed archive split into several parts. The benefit of this being that by splitting a single archive into numerous parts, you can store the archive in chunks across multiple disks.

With each section of the split archive being given a corresponding extension i.e. C01, C02, C03, and so on.

WinAce is 'archive management' software, allowing you to backup and compress data, reducing file size, which is beneficial for data storage or for data transfer over the internet, etc.