When most* Christians think of Hell, they think of a place of physical torment where people suffer throughout eternity for the sins that they have committed or simply for failing to accept Jesus as their savior and as the one true God. In that sense, Hell is a place of external affliction for your past actions.
For Buddhist, hell can mean two things. One, hell is a direct result of your negative actions. It isn't so much a external torment as it is an internal torment. We crave, we desire, we seek to hold that which we cannot, and we suffer because our craving goes unfulfilled. The more that we want the more that we suffer. Hell is not a place that one goes per se, but more a state of being in which one exists. The mental anguish that we cause ourselves is generated through our own actions. For many, this aungish is so great that it can be described as hell.
The second way hell can be described for a Buddhist is that because of our craving leads to immense negativity, we ultimately put ourselves in places of physical discomfort and pain. It is this fundamental clinging that leads us to places where it is harder to find mental harmony and stability. When we die, this clinging has a more profound affect. As the physical nature of our existence disipates, our minds (loosly used) begin to rage, looking for things to hold on to and this effects the cycle of rebirth.
*I use the term 'most' because during the enligtening period, many Christian scholars moved towards a different understanding of Christianity and what Jesus meant with the 'Kingdom of Heaven'. Some Christian monks still follow this alternative view but mostly it is just discussed in scholarly circles.