This error can be caused by several things, but two common problems are:
1. The MapPress server couldn’t be reached
2. The plugin directory can’t be deleted – sometimes WordPress seems to apply invalid permissions to the plugin directory.
For #1, just retry the update.
For #2, try deleting the plugin directory using FTP (your maps won’t be deleted). Then reinstall from your account (there are installation instructions on the same page): http://mappresspro.com/account