One conception is of eternal suffocating heat, being taunted by demons for all eternity.
Another conception, derived from the scripture about Gehenna is simply that people will be discarded (burned), as being unworthy of preservation by God.
In both conceptions, Jesus is accepted as the Lamb of God, able by perfect sacrifice to atone for one's sin, though one is required to accept Him. This acceptance is said to constitute salvation from sin, and therefore from damnation (though a debate exists between Christians over the role that works play in salvation).
In Eastern Christian traditions (Eastern Orthodoxy and Oriental Orthodoxy), it is not seen as a legalistic punishment meted out by an angry and vengeful God for a slight against some set of spiritual rules. Instead, it describes a state of separation from God, a state into which all humans are born but against which Christ is the Mediator and "Great Physician".
"Damnation" (or, more commonly, "damn") is widely used as a moderate profanity. Until around the mid-20th century damn was a much more offensive term than it is today (its usage in the film Gone With the Wind in 1939 shocked some audiences), and was frequently represented as "D--n," "D---," or abbreviated to just "D."
Instead, it describes a state of separation from God, a state into which all humans are born but against which Christ is the Mediator and "Great Physician".
"Damnation" (or, more commonly, "damn", or "goddamn") is widely used as a moderate profanity, except in the Southeastern USA where "goddamn" is considered extremely offensive.
Until around the mid-20th century damn was a more offensive term than it is today, and was frequently represented as "D--n," "D---," or abbreviated to just "D." The use of "damn" in Rhett Butler's parting line to Scarlett O'Hara in the film Gone with the Wind in 1939 captivated moviegoers.
And goddamn you, Richard Cheney and Donald Rumsfeld and Karl Rove and Condi Rice and Antonin Scalia and Clarence Thomas.
Goddamn you for having rigged our democracy and Goddamn you for having made the world more dangerous for my innocent son and the children of millions of other Americans who will reap the whirlwind from your deeds today.
Goddamn you for lying from Day One of your insurrection in January 2001 and Goddamn you for what you plan to do in 2004 to deny what's left of our democracy's dignity the right to resoundingly toss your asses out on the sidewalk.