-C - automatically determines how to resume the transfer, based upon the input and output files.
man curl (note the second paragraph):
Continue/Resume a previous file transfer at the given offset.
The given offset is the exact number of bytes that will be
skipped, counting from the beginning of the source file before
it is transferred to the destination. If used with uploads,
the FTP server command SIZE will not be used by curl.
Use "-C -" to tell curl to automatically find out where/how to
resume the transfer. It then uses the given output/input files
to figure that out.
If this option is used several times, the last one will be