Back in the 14th century, billiards—or the game's forerunner—was originally played outdoors, on the lawn. It was similar to croquet, in that a ball was propelled by some sort of stick (there were many variations: curved, flat, elongated, etc.) around and through a series of arches and pegs. There was usually a target of sorts, perhaps a cone-shaped object, which players tried to knock over. It was mainly played by royalty and the nobility, which is why it was eventually moved indoors; it protected them both from the weather, and from any hostile locals that had a governmental overthrow in mind.
Written records are sketchy, but it is believed that the French were the first to get weary of bending over, and moved their cue sports onto a table. (A billiard table was listed in a 1470 inventory of King Louis XI’s royal possessions.) The game evolved over time, and rubber bumpers and “pockets” were added to the game table. But the green felt covering has remained consistent, as a nostalgic nod to the original grassy playing field.