In most cases the issues with importing demo content are caused by server php settings.
Hosting providers sometimes limit server resources, so they can have many clients on relatively small server hardware setup.
Importing content together with images takes some time and if there is a time limit set, the process gets killed on the server before the content is imported.
In most cases there is an issue with max_execution_time settings in php, which prevent import to finish. Sometimes also memory_limit or upload_max_filesize are preventing the import to finish.
All of these three are just a simple PHP setting, which can be set by editing php.ini file.
Recommended values are:
max_execution_time = 600
memory_limit = 256M
upload_max_filesize = 32M
upload_max_filesize = 32M
If you are on shared or similar hosting and don't have the access to this setting, than you will not be able to solve this by yourself. You will have to contact the hosting provider. Mostly they help when contacted with such request.
If they agree to raise this limit, this is the best and least painful solution for the demo import problem.
Before importing the content again, We suggest to first delete everything on your site, using a plugin like reset wp.Warning: this will delete all your content.
What to do, when hosting provider doesn't want to help with the issue?
1. Having a hosting provider, on which you can rely on, is important. You might want to consider switching to a better one, because a day might come when you will need their assistance on a more crucial matter.
2. You can also try to set the site on your localhost using tools such as Wamp (Windows) or Mamp (Mac) and import the demo content there. When the import of demo content is finiched, you can just export the MySQL database and import it to the server using phpMyAdmin. Separating the development and deployment is the most common workflow in the web agecies.
For moving the Wordpress installation to the server, this article on wordpress.org should be helpful.