The “six worlds” refers to the bottom six worlds of the ten dharma realms, i.e., the world of sense desire which includes the hell realms, the hungry ghost realm, the animal realm, the realm of asuras, the human realm and the realm of the gods of the sense desire world. A sentient being in any of these six realms is subject to visiting the other five realms in one lifetime and is subject to re-birth in any one of the six realms. Only the sentient beings of the top four realms are immune to falling into the world of sense desire.
To confuse matters a little more, the six worlds is also referred to in the sutras as the first of the three worlds, i.e., the world of desire. The second world is the world of form, attainable through the jhanas, and the third world is the world of formlessness, attainable through the immaterial attainments. We will encounter “the three worlds” and “the ten directions” in the chant which is used to close a chanting session. The ten directions refers to North, Northeast, East, Southeast, South, Southwest, West, Northwest, Up and Down. Go figure.