Chests contain a variety of useful items that can help you play the game including Gold, Gems, Cards, Golf Balls and more.
Broadly, they can be categorized into Star Chests and Pin Chests.

Star Chest - Available in Silver, Gold, or Platinum. Star Chests can be opened by filling the gauge bar with Star Points which can be obtained through gameplay.
Pin Chest - Golfers are awarded a Pin every time they sink a ball into the hole. Collect pins to to open Pin Chests.

Additionally, a King Chest can be obtained if you come in 1st place in the Tournament or your League.