Am trying to backup my databases through the terminal in Ubuntu using the mysqldump command and it's successful , but where does it place the backed up databases ?
Usually you use mysql dump like this
mysqldump -h host -u user -ppassword dbname > dumpfile
So the output is whatever file you redirect output to. The output file will contain instructions that will rebuild the database from scratch, including the schema, if your run it on a new install like so.
mysql -h host -u user -ppassword dbname < dumpfile
Here's wiki on IO redirection