This problem often occurs because one of the default settings of WAMP is too low. You'll see the issue if you go to the MySQL-controlling phpMyAdmin screen (probably at http://localhost/phpMyAdmin) and click "Import": The maximum file size allowed is 2,048K. That's only 2MB, and the databases for most Drupal sites are much larger than that. (The example site for Drupal Essential Training gets as big as 5MB.)
To change this limit:
- Click the WAMP icon in your system tray.
- Select "PHP". In the side menu, select "php.ini" to open a file containing PHP's configuration options.
- Search for the line, "upload_max_filesize = 2M".
- Change it to "upload_max_filesize = 64M" (or whatever you like). You can get by with as little as 32M, but I recommend at least 64M, particularly for Drupal 7.
- Save the file and restart WAMP. (Better yet, restart your computer entirely to be sure. I'm frankly not sure whether it makes a difference.)
- Now go back to that "Import" screen in phpMyAdmin: You should notice that the limit has changed.
Thanks to L.H. for pointing this out!