Damnation to hell is the punishment of the Christian God for persons with unredeemed sin. Damnation is a primary motivator for conversions to Christianity.
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 Christ 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).
"Damnation" (or, more commonly, "damn") is widely used as a moderate profanity.