As a boss, how can I explain to staff why I had to fire one of them without demoralizing them?

Explain that the individual who was fired was not maintaining the standard and was a detriment to the rest of the team.

You can always explain that this action is the result of restructuring and synergy within the organization. Although you would have liked to see more solid improvement in the worked they performed the new direction in the company is moving is the end result of their being released from their duties.

You need to talk to your HR team for the right steps forward. In general, the person being fired should require little explanation. You should have already worked with them on an improvement plan, set goals for improvement, and made it clear that termination would be a consequence. You would have already had to make it clear that the goals were not met. The firing conversation should be as simple as "We set a plan and unfortunately you didn't hit the goals we agreed on. I know you'll do a great job at your next opportunity, but your work here ends right now." If you are explaining to the remaining team why you fired someone, then you have to be very limited in what you say. Tell the team that the person will not be with the team anymore. Tell them that you can't go into specifics. Reassure people that you will do what it takes to get help with the fired person's work. Remind them that they all meet and exceed the standard that they need to, and that you value them. Good luck!

I do not think you need to explain the why. Just the person is no longer with the company, and explain what will happen to the duties they were performing.

Explain clearly and professionally that you had to let them go.

Ideally the person being fired should be give advanced notice and understand their performance is lacking and after improvement plans aren't showing positive signs, the employee should be given an opportunity to move into another group or find a new company (say 8 weeks) where they can leave with gracefully with a new job

Make sure they have plenty of chances to get their act together

I tell them that Human Resources information is always confidential. I say, “you would want me to do the same thing for you, right?” I also explain, if the person was popular among his or her peers, that the employee was two different people: the person we knew at work and the person we love as a friend. We still love the person as a friend, we just won’t be working with them anymore. It is never easy. Good luck!

Well if you have to explain it to them then they probably should be fired too but if they're their employees they probably know why he's being fired anyway

As a boss you have to show great empathy in how the removal of one of them has and will effect you as one of them and as the boss, and the firing of one of them has left you with great sadness as well.

Explain the reasons for letting the person go, the steps you took (hopefully) to work with that person to help them function at a level that would have helped them keep there job.

Explain the real situation, make it clear you are still batting for them. Don't make it seem like roses, understand and express how it sucks. (Depending on why they were fired.)

You tell them it sucks you had to let one go but if you didn't let that one person go, later on it might end up being all of you that have to find a new job when the company starts to fall apart.

Assure them it was not working with this one person.