Ancient Greek temples were built in order to house the many sculptures of the various deities. The ancient Greeks used the temples as the sacred place whereby they would be able to leave specific types of offerings. Depending upon the wealth and status of the individual, these offerings might include flowers, food, personal valuables, jewelry, oils and incense. The architecture of the temples reflected the respect and deference that the ancient Greeks had for their pantheon of Gods. These temples served as the link between the sacred and the secular in ancient Greece, and as such played a significant role in the ancient Greek society.
Because if they didn't, they'd fall down! Okay, okay, I couldn't resist!
I would think the they built them to celebrate Nature--the temples would be man-made imitations of the gods' majestic realm--the columns the trees, the stones the mountains, the fluid designs of streams, the spacial freedom of air--artistic creations of living spirit, spiritual creations of artistic life. Temples posed the awe, echoed the spirit, drew the man, and formed the community in the communal Greek spirit of pietas. The Greeks built Temples to elevate the ethereal with the visual, to mark mythic labour with details of structural composition, to echo the harmony of universal balance, and with measured details, to embrace the beauty and order of the universe-- with a suite sweet enough for a god.
The greeks build temples to make a home to their gods, to honor them, and also to worship them.