It means that you didn't do anything wrong but you're fired because someone doesn't like you, or some manager is mad about something and needs to fire someone to make a point. So don't say anything about it because we don't want to deal with bad publicity or potential legal problems.
It actually happens MOST of the time in professional contexts.
"Severance" is usually no big deal, it's like 1-3 months worth of paychecks.