Funny you should ask. I actually am an integrated circuit designer and am designing in 28nm right now. However, I do analog design, that is, amplifiers and bias circuits and PLL's etc. not computers.
22nm means twenty-two billionths of a meter, or just under a millionth of an inch. That is the gate length of the CMOS FET's, or transistors in the chip. To simplify things, the gate length is the distance between the two contacts in the logic switches. The lower that distance is, the smaller, faster, and lower the power of the logic switches are and hence, the faster and lower power the processor is. 14nm, or a bit more than one two millionth's of an inch.
Now how this will effect gaming is a whole other question. The subject is very complex and involves quantum mechanics and all, but, basically, making transistors smaller and smaller is getting harder and harder. The cost is rising, and the benefits are shrinking. Way back in the 80's when we went from , say, 2um to 1um (two millionth's of a meter to one millionth's of a meter), the area of the chip was more than halved, and the performance was doubled, at least. Now, because we are hitting the limits, those gates are only a couple dozen atoms long now, weird stuff happens and you no longer get the response you want. One advantage for sure is lower power.
To boil this down. 14nm will be lower power and faster, but not a whole lot like the good old days. For most games around now, this extra processor power won't be needed. However, some new games, like Crysis 3, really requires a lot of processor power. So, by the time we see Broadwell, summer2014 or later. Perhaps many games will need extra processing power. Keep in mind though, Intel seems to be going after lower power, rather than greater processing power.