I know this is called the Flynn effect and that average IQ scores went up significantly across most of the last century. What I do not understand is why this happened if intelligence is supposed to be largely genetic. And I have also heard that the effect has slowed down or even reversed in some countries recently. Is that true and if so what does that tell us about what was actually driving the increase in the first place?
The Flynn effect is one of the most studied phenomena in psychometrics and the explanation that has held up best is that it reflects environmental gains rather than genetic change, since genetic shifts happen far too slowly to explain score increases over just a few decades. The leading factors include improved nutrition, especially reductions in childhood malnutrition and disease burden, smaller family sizes, increased years of schooling, and a general shift toward more abstract reasoning demands in modern life.. 
The fluid reasoning concentration is the detail that convinced most researchers this was environmental rather than genetic. A real genetic shift would not selectively boost one specific ability cluster like that. Environmental causes that target early brain development would.