Civilization V streamer BabaYetu uses a time-honored technique to try and milk the most out of an ancient ruin that his warrior (his southeastern unit) finds. Each ancient ruin contains a one time random bonus, which can be an instant extra citizen in the nearest city. Mechanically, this bonus gives the city exactly as much food as it needs to grow to the next size. Thus the free pop is less valuable if your city has stored food for growing the next pop, and more valuable if you’ve just grown and are at 0% towards yet another pop.
On turn 5 at the start of the clip Amsterdam is only one turn away from growing naturally, so getting a pop ruin would not save very much food. By waiting one turn for the city to reach size 2 on its own, Baba gives himself chances for a pop ruin to boost him all the way from from 2 to 3, saving 8 turns.
In this case, the ruin contained “evidence of recent barbarian activity” (the worst of the possible bonuses). Still, Baba played accurately by setting himself to get the most value in case it were a pop ruin. The idea behind the play is related to the concept of “playing to your outs” used in Magic: The Gathering strategy. Luck favors the prepared.