I'm going to migrate my site to another server. so, i need to backup my database if i dump my database using
mysqldump command into backup folder. does database manage it by updating the changes done into database to the sql file.
No, the database does not update your dump-file afterwards. You should prepare your new site with a database dump.
Then when you are ready to move the site finally you should put your original site in maintenance mode, and dump and import your database with the latest content. In this way you ensure that you will get the most recent content from your old live site.