Things that are elusive are hard to find, pin down, or remember. They slip right out of your grasp.
Ever try to catch a mouse? It's not easy, because mice are quick and elusive — they're tough to catch. Rabbits are speedy, so they're elusive too. Also, things that are tough to understand or describe are elusive — like the concepts of love and beauty. If you had an idea and then forgot it, the idea is elusive: it slipped away. Anything you can't get hold of, with your hands or with your brain, is elusive.