Since the database is huge, it can't be downloaded through phpmyadmin.
To download only through phpmyadmin, additional parameters like: php execution time limit, mysql time limit, mysql cache size etc etc needs to increased in files like php.ini mysql.ini
Instead mysqldump can be used.
Login to your site using SSH. Eg:
>>ssh user@your_website.com
>>Enter password: your_password
>>mysqldump -u [uname] -p[pass] [dbname] > [backupfile.sql]
[uname] Your database username
[pass] The password for your database (note there is no space between -p and the password)
[dbname] The name of your database
[backupfile.sql] The filename for your database backup