seems you missed a space to specify which path is source and which is destination.

cp -r /home/user/ /media/mmc1/backups/

this will recursively (-r option) copy the contents of users home dir to the mmc card, in a folder called backups that must exist prior to running the command. note the space between user/ and /media. i am not sure why your are specifying a file name for the backup, though.