"Cycled" is a term for completing a lap of the "nitrogen cycle" as graphically displayed in the IBC of AP. Ammonia is converted into nitrites, then nitrites into nitrates. When your system starts lets assume there are minimal naturally occurring beneficial bacteria in the system, so we need to feed them with a little bit ammonia in the first place. This will be converted into nitrites and then a second naturally occurring bacteria will convert this into nitrates which are readily used by your plants.
When any added ammonia is completely used, and any generated nitrites are completely used then your system might be considered cycled. Personally, I add a time factor; when all the ammonia and nitrites can bve converted to nitrates within 24 hours then I call this "fully cycled"
Read more in the free "IBC of AP" http://www.backyardaquaponics.com/Travis/IBCofAquaponics1.pdf
Water Turnover: a general rule of thumb is that you want to pass all of your water through the GB once per hour, so if you're only completing a water "cycle" in a week, then you're going to need a much bigger pump!
If you're going to run your system as continuous flood then you need about 600LPH pump (discounting the effect of any head losses and assuming you chopped a single IBC to build your system), or if you're going to use a timed flood and drain, then you're going to need something in the vicinity of 2000-3000LPH for a 15on/45off cycle (although I have seen smaller pumps effectively used in IBC systems)
Again, there's lots of information in the IBC of AP book.
Scott