Gehennom is roughly the Jewish equivalent of a Christian Hell. According to the Talmud, the average soul after it leaves the body goes to Gehennom for 11 months (this is why it is customary for one who's parent died to say kaddish for 11 months after the shivah) where the soul is "purified" before it can enter Gan Eden roughly the Jewish equivalent of Heaven. A person who is excessively wicked goes to Gehennom for 12 months or, if he is very evil, can stay there forever or even have his soul destroyed. Contrariwise a person who is very righteous can avoid going to Gehennom entirely. While it is important to understand that there is no physical or tangible element to Gehennom I have heard the torture of Gehennom comparable to being suspended by ones feet and descending into boiling excrement.
The Talmud teaches that there are three people who go straight to Gehennom after dying. They are: the thief, the one who shames his friend in public, and the one who calls his friend by a bad name.
A Rabbi once explained the soul in a very helpful way. He said the soul is a clean white shirt. With every sin we stain that shirt differently. Gehennom is a laundromat. It's not easy, but we scrub ourselves clean because Gan Eden is an audience with God and a chance to experience pure joy.
I have heard one other analogy. The soul is a battery. When it cleaves to the body its potential expires. God is a power supply. Gan Eden and Gehennom is simply the act of recharging your soul. Now imagine the afterlife as a an amphitheater with God as the centrepiece. When we recharge we attach a straw to God through which we suck our potential. Depending on a person's relationship to God, a soul can cleave better to God in the afterlife. Gan Eden and Gehennom are simply how close you are to God and how fast you can reenergize you soul.
This coincides with a Chassidic parable of the afterlife. Envision a long table with the righteous on either side on the left and the wicked on the either side of the right. Placed before each person is his favourite food, the only catch is that no one can bend his arms. The righteous feed each other, the wicked learn to share or starve.
The reward for a good deed is the chance to do another.