The general point about the birth certificate is that it is a requirement that the President of the USA has to be born in the USA. Thus, for example,Schwarzenegger could never be President even if his political ambitions lay in that direction.The question was posed by Republicans in order to undermine the legitimacy of Obama's presidency.
The ironic thing is, if you go back to the 2008 election, his opponent, John McCain, was the one who could have been questioned on this score. McCain was actually born in the Panama Canal Zone, his father having been posted to the US Navy base there, with his family. Whether that base was sovereign US territory at the time McCain was born, I do not know but it is clearly outside the states that make up the United States.
Personally, I did not then, and do not now, question McCain's legitimacy as a Presidential candidate, whatever the legal niceties involved. IMHO, there was a certain hypocrisy, on the part of the Republicans, in challenging Obama in this way and I find it difficult to put out of my mind the thought that, underlying this challenge, was an element of racism.