This is not just to make it easier on the person being fired, though that reason alone is good enough. If the situation does degenerate into histrionics, be prepared for your team to get spooked. As manager, you must stand firm when the newly jobless break down into tears. But you can't ask the whole team to stand by and pretend to work while it is happening. After the fired person's tearful departure, discuss the situation with the team as openly as you can while still remaining diplomatic.
Different companies have different rules for severance packages.
Personally, I opt for having employees cash out instead of lingering for several morale-wrecking weeks. Although a shade Orwellian, coming in the following morning to find a clean desk is generally more acceptable than finding a dejected friend listlessly sending e-mails to agencies and friends. Of course, the best way to avoid a firing is to make sure you hire the right people in the first place. You can't always get it right, but an effective interviewing process can reduce the occurrence of firing. If you have any doubts at all about a candidate's suitability, don't hire them.