Working " on call pool" meaning ? being a nurse?

Even I in the U.K. understand that.
You will not have a permanent job but will be called in when needed for a 12 hour shift.
Could be 5 days a week, or one or none.

I would interpret "full time hours" to mean that when you are called in, it will be for a full shift.  It does not mean that you are regularly scheduled though, because that is the very opposite of being on call.  You will be a replacement for a full-timer so you will work a full shift when you work.  Like a substitute teacher, basically.

Pool nurses fill in where needed- when another nurse is out sick, for example. It means you won't be permanently attached to one section. However, in most places, nurses are in such demand that you will almost certainly get 3 12 hour shifts a week- making it a full-time position. 

Ask again.  As far as I understand it, you are not being offered a regular, full-time job.  You are being "hired" but your shifts will be as needed.  Your name will be among a pool of other nurses who will also be "on call" to be called in as needed.  You will be paid either a per hour rate at for the days you work or a per day rate.

On call - You get paid (a daily wage but not normal pay) to sit by the phone and be ready to be called to work in case there is an emergency, or somebody doesn't show up, etc.

Pool - they have a whole bunch of people doing it.