A 'birther' is someone who questions whether President Obama was really born in Hawaii, USA. The significance of this is that a US president must be born on US territory (ruling out Arnold Schwarzenegger, for example) . The 'evidence' for this theory is that no birth certificate has ever been shown to the public (though other documentation has).
'Truther' question the official description of 9/11 as a terrorist attack, suggesting many improbable alternative theories, usually involving government conspiracies. The rationale for these rests on unusual aspects of the event - the fact that one of the adjacent towers survived relatively unscathed.
Birthers are associated with the right of American politics, though rejected by most Republicans. The 'truther' movement has its origins on the far left, with some of its exponents claiming that Israel was mysteriously involved. There are, however, exponents of both views closer to the mainstream - potential presidential candidate, Donald Trump, is the best known birther, while one of Obama's 'czars' (Van Jones) was forced to resign when his truther views became public.
Perhaps the common denominator is extreme skepticism about 'official' history - this trend can perhaps be traced back to Watergate or even the 'second shooter' theories regarding the Kennedy assassination.
Update: A day after this post President Obama produced his birth certificate at a press conference - ending three years of speculation about it. The power of English Language FAQ! Now all we need is for Al Queda to confess to 9/11 - no wait a minute they've been boasting about that vile act for nearly a decade ....