Luxuriant means "characterized by thick or abundant growth." It is usually applies to the growth of plants, fur, or hair. The noun form is luxuriance.
Luxurious means "characterized by wealth and comfort," more directly from our modern word luxury. The noun form is luxury or luxuriousness.
Examples: Captain Cook named the place Botany Bay because of the luxuriant jungle vegetation surrounding it.
They checked into the most luxurious suite in the hotel.