A one gigabit port in full duplex means that it can send and receive one gigabit per second in both directions. The back plane of your switch / router / whatever is what controls how many of your ports can be used concurrently.
If your back plane supports 1 gigabit per second you can have computer A copying a file to computer B at 1 gigabit per second but nothing else active (not copying from computer B to computer A or anything at all between computers C or D). If your back plane is 8 gigabits per second all four of your ports can go in both directions full blast all the time. The more capacity in the back plane the more expensive the switch / router becomes.
Please note that this is probably overkill for your network - if you aren't familiar with the duplex and back plane theory you likely will not produce enough load on your network to require it. If you only occasionally want to copy large files pretty much any gigabit switch / router would do the trick.