Hi Judy,
You are correct that Judaism doesn't believe in "eternal damnation".
However, we DO believe in punishment for sins.
There are mixed explanations for what "hell" means in Judaism.
The most commonly believed explanation in Judaism is that "hell" or "Gehinom" is where sinners go. After a person dies, he is judged by G-d, and if he is deemed to be a "good" person, he goes to "Gan Aiden" or the Garden of Eden, there to bask in the glory of G-d and to study His Torah at His feet. If he is judged to have been "bad" he is sent instead to "Gehinom", where he spends up to a year expiating his sins through suffering. After that one-year period, he then goes to Gan Aiden. That is why mourners say kaddish for a dead person for 1-year, and then only on the anniversary of the death.
(Note: This is true for most "garden variety sinners". The TRULY evil --- ei: Hitler--- stay in Gehinom forever. But such levels of evil are truly rare and are very much the exception to the rule.)
Nachmanides gives a slightly different explanation. He says that Gan Aiden and Gehinom are the same place. If we are good, we go to that place, and we find comfort in that place. If, however, we are judged "bad", the embarrasment and shame of being close to G-d while being in that "evil" condition is so painful that we suffer emmensly for it. It takes time--- up to a year for most people--- to get past that shame and humiliation and come to a level of feeling comfortable in G-d's presence. Our sins are, therefore, expiated by that shame and humiliation. The truly evil, of course, never get past that shame. The key point, though, is that "heaven" and "hell", according to this interpretation, are one and the same. It is OUR CONDITION that makes the difference in how we experience that place.
What is the truth? Who knows. It is said in the Talmud that only 4 people ever entered Pardes (G-d's Presence in Heaven) alive. One died, one went insane, one became a heretic, and the 4th, Rabbi Akiva, entered whole and left whole, but never spoke of what he saw there. So the answer is that we really don't know what the true nature of heaven and hell is. What I have described above are just concepts, and very basic ones.
Hope this helps.
Elliot