Once fired how does it effect your future in working for the company?

It's better to schedule an "Exit Interview" with your manager and Human Resources, as they won't give you any accurate statement on the day of your leaving, about whether or not you'd be hired again. In that interview, you can ask specifically what you could have done to demonstrate professional growth; and review your evaluation(s) to see if those were objectives given to you beforehand. If there is a union that represented nurses where you worked, be sure to have a rep there, or someone who could be objective (not your mother or anyone who works there), to hear what goes on. Be sure that doesn't become this :argue:

Time heals a lot. Maybe in 10 years you'll have sufficient work experience to show growth.....

Most firings result in "Do not rehire", which remains in computers for a predesignated length of time. The personnel folder is in a locked "dead" file drawer for at least 2 years, usually.

So it's best to look elsewhere for employment, knowing that you can list that employment on your resume, but it would be most unwise to give as a reason for leaving, that it wasn't a "good fit". That phrase is too commonly used by employers as a reason for firing. Experience is experience, and you can be reassured that only your time there will be revealed, when inquiry is made, and that's usually in writing. If you got a good eval while there, include a copy of it with your application.

I wish you lots of good employment experiences in the future!

I was fired for not progressing well (New Grad) at least that is what the named it on paper. But what if I wanted to work on another unit or at a different hospital that the company owns? Is human resorces realistic? I mean nurses move around all the time making it easier for nurses that left or got fired to come back to a better work environment. Am I banned from ever working for them again once I do get experience?

I dont think they would ever hire you back, sorry.