It's usually spoken casually when someone is proven wrong, but only when the person is defeated, or surprised. In the case of being defeated, "I'll be damned" shows that you accepted the loss. You can think of it like two people betting on who will win a race. The loser, once the race is over, would probably say this due to losing his bet, or because he was surprised he lost. You would never say it, however, if you were expecting to be proven wrong.

It means: "I'll be surprised." Although the tense in the sentence "I'll be damned" is the future ("will be damned") the sentence can refer to something that has already happened, is happening, or will happen. And as Mockingjay27 mentioned, the word "damn" might be offensive to some people. It is an expletive (swear word).

I agree with Jkduzz, but "damn" can take on a negative meaning when used in conversation so I wouldn't say it with people you don't really know.

En México lo usamos como una expresión cuando se hace alguna promesa o un juramento. Por ejemplo; Te lo juro por mi mamá, "que me parta un rayo" si estoy mintiendo. Te prometo que llegando a casa te marco si no "que me parta un rayo"