The law of large numbers basically says if you do something involving randomness enough times, the average result will tend to become more predictable.  For example, when flipping a coin, while any single flip has a 50/50 chance of being heads or tails if you flip it a thousand times you'll likely end up pretty close to 50% heads and 50% tails overall. 

The gambler's fallacy comes into play when people think that short-term deviations from that long-term probability somehow need to correct themselves quickly.  Like if you flip 8 heads in a row, the next flip should be more likely to be tails to balance it out.  But that's not true - the odds are still 50/50.  Each flip is independent.

People struggle to really grasp how long you sometimes have to go before probabilities truly even out in random systems.  They underestimate how long the long term can really be - it could be thousands and thousands more coin flips before you see that 50% rate emerge.  People are bad at intuitively understanding true randomness over short time spans.