This is a common issue with the WordPress Importer. As MESH's demo content is pretty big you will need to set your server to support the size of our .xml files.
In order to make this work you need to speak with your hosting support (they will know what to do in 99% of the times) and ask them to increase:
- your wordpress upload size limit
- max_execution_time to around 300
- max_input_time to around 300 as well
Remember that to import the demo content you need to go to Tools -> Import -> Wordpress and choose the .xml file for the MESH demo you wish to install.