Samsara is this world, filled as it is with so much pain and sorrow. All beings in this world are subject to the law of karma. Karma means volitional act, that is, something you do, say, or think that is in fact in your control. Any such act has moral consequences, called vipaka, which means fruit. In traditional Buddhism, this consequences can occur in this life, or in a future life.
Most Buddhists believe in rebirth. For many, rebirth is no different from what the Hindus believed, i.e. reincarnation or transmigration -- moving from ones old body at death to a new body at birth or conception. A little more precisely, rebirth is nothing more than the transmission of ones karma. Buddha likened it to the flame that passes from one candle to another. So the idea of an immortal soul, a continuing personality, is definitely not part of the rebirth idea.
Rebirth and similar concepts are not a part of most westerners cultures, so many western Buddhists, as well as some eastern Buddhists, take rebirth as a metaphor, rather than literally. Buddhism has never been a particularly literalist religion, so this is not at all taboo. In fact, Buddha often avoids discussing the reality of one metaphysical idea or another as irrelevant to the practice of the Dharma.
The Tibetan Wheel of Life represents Samsara. In the very center, there is a rooster chasing a pig chasing a snake chasing the rooster -- craving, hatred, and ignorance. Around that are people ascending the white semicircle of life, and others descending the black semicircle of death. The greatest portion of the Wheel is devoted to representations of the six realms -- the realm of the gods, the realm of the titans, the realm of humans, the realm of animals, the realm of the hungry ghosts, and the realm of demons -- each realm looked over by its own boddhisattva. The outermost circle is the 12 steps of dependent origination. The entire Wheel is held by Yama, the Lord of Death.
The ten fetters, or Samyojana, bind us to samsara.