It's because by default, watch itself wraps your command in a sh -c command. This means that you lose a level of quoting, and your command becomes

sh -c df -h | grep sdc

so that sh -c executes plain df, with -h being passed as a positional parameter to the shell.

You can either add additional quoting:

watch "sh -c 'df -h | grep sdc'"

or tell watch not to wrap the command using -x:

   -x, --exec

          command is given to sh -c which means that you may need  to  use

          extra  quoting  to get the desired effect.  This with the --exec

          option, which passes the command to exec(2) instead.

or simply run

watch "df -h | grep sdc"

without the (unnecessary) explicit sh -c.