This word originated in the USA, probably in 2004. No one is sure who first used it, but it was noted in online dictionaries in 2005.
Libtard is an insult used by rude right-wing people with closed minds to characterise those who display a left-wing belief.
As should be obvious to the meanest intelligence, insulting people isn't an intellectually valid way to convince anyone of anything.
It's quite a good way of both hurting people and starting a fight, though, if that's the kind of thing you enjoy.
Sunday Rest: libtard. This horrid word is made up of liberal and retard. The Latin word līberālis means of freedom (so it's by no means exclusively a characteristic of those of the Left). The word retard, meaning to slow down, comes from the Latin word tardāre, to make slow.
Retarded, in some parts of the world, means disabled, so it needs to be used with care.