rsync -cav --delete --progress "/dir/A/" "/dir/B"
Some explanation on what the various command options mean:
-c, --checksum skip based on checksum, not mod-time & size
-a, --archive archive mode; equals -rlptgoD (no -H,-A,-X)
-v, --verbose increase verbosity
--delete delete extraneous files from dest dirs
--progress show progress during transfer
Note the ending slash in the first directory path above ("/dir/A/"). The above command will make directory B the same as directory A, DELETING any file in B that is not present in A.