My understanding of this is that, as the code flows through a single turn for a given city, most yields (like food) are calculated before a new citizen is born, but production is calculated after the new citizen is born. So by having the focus set to "production" the new baby will be sent to the "hammeriest" available tile, and the city will benefit from those hammers immediately, on THAT turn. If the citizen were to be directed by any other focus (food, faith, science) to a tile with, say, only one hammer, you would get that one hammer, but you wouldn't get the other yields on that tile until the next turn.
I usually want my citizens working food tiles. But by using this micro-management, I get a little bit more production for every birth. But then, you DO have to remember to click every "new birth announcement" to take you to that city to put the citizen where you really want him. (After a while that becomes a reflex!)
You don't lose anything by not doing this, you just get a little more benefit when you do.