Play Coins are new feature to the 3DS, and are earned by walking around with your 3DS in sleep mode.
Similar to the Pokewalker addon for the original DS, the 3DS has a built in motion tracker that will count your steps while the 3DS is in sleep mode. Nintendo seems to be into trying to get kids active by giving them these incentives.
You earn them fairly quickly, at about 100 steps per coin. The value of the coins depends on the game. Some games so far only need about 20 coins to unlock certain items.
There is a cap on the amount of coins you can have at once, which is currently set at 300 coins.
Honestly, 100 steps isn’t that much and you can rack up these points fairly quickly just by your normal day to day walking. So, put your 3DS into sleep mode and throw it in your pocket and go about your business to earn as many points as you can.
Or.. tie it to your little brother or your dog (be careful with this one) and sit on the couch watching your points go through the roof.