Backup a single table from the database:
mysqldump -u -p database_one table_name > /var/www/backups/table_name.sql
Restore the table into another database:
mysql -u -p database_two < /var/www/backups/table_name.sql
mysqldump -u -p database_one table_name > /var/www/backups/table_name.sql
mysql -u -p database_two < /var/www/backups/table_name.sql