For example, if a directory listing finds makefile when git expects Makefile, git will assume it is really the same file, and continue to remember it as Makefile. If true, this option enables various workarounds to enable git to work better on filesystems that are not case sensitive, like FAT.
For example, renaming a file in a way that only changes letter case will cause git to report spurious conflicts or create duplicate files (from Mark Amery's comment). Note that setting this option to false on a case-insensitive file system is generally a bad idea. (Be careful if you have already pushed the files, then you should first move them given the other answers). To tell Git to be case-senstive, simply set this setting to false.
Git has a configuration setting that tells it whether to expect a case-sensitive or insensitive file system: core.ignorecase.
