This is a package requested by, at the least, the Coder Tough Love Drupal module.
Searched around for a fix to the error message on the coder tough love settings page that there was nothing to configure because it didn't have the pspell package installed, nothing at results for ubuntu pspell, enable pspell, php5-pspell, enable pspell linux said exactly what to do.
Naturally...
sudo apt-get install php5-pspell
sudo /etc/init.d/apache2 restart
is all you need on Debian / Ubuntu.
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