The obvious significance is that the treaty established the non-Christian nature of the United States. In fact, Article 11 of the treaty, from which the President quoted, reads, in its entirety:
The point that he was trying to make with this is that America has always been open and tolerant of Islam. Well and good. Point taken.
As the Government of the United States of America is not, in any sense, founded on the Christian religion; as it has in itself no character of enmity against the laws, religion, or tranquillity, of Mussulmen; and, as the said States never entered into any war, or act of hostility against any Mahometan nation, it is declared by the parties, that no pretext arising from religious opinions, shall ever produce an interruption of the harmony existing between the two countries.
The other, hidden part of this is the darker underbelly of the true statement that "Islam has always been a part of America's story". The Treaty of Tripoli was a capitulation to privateering. American ships were being captured in the Mediterranean, so the nascent US concluded a "treaty" with the Barbary States in which they agreed to pay a certain amount per year for "protection". Article 10 of said treaty states:
The money and presents demanded by the Bey of Tripoli, as a full and satisfactory consideration on his part, and on the part of his subjects, for this treaty of perpetual peace and friendship, are acknowledged to have been received by him previous to his signing the same...That's the obscure part. Of course, this was before the US even had a navy. Once they got one, they went and kicked some Tripolitan a** (that's the "... to the shores of Tripoli" part of the Marines' Hymn). So what was he trying to say? Was he trying to reinforce a 200-year-old US policy of capitulating to what was essentially state-sponsored piracy? Was he trying to say that the US can take a bit of thuggery here and there, but don't press your luck? Or am I being too intertextual about this and it was simply an observation that the US and a Muslim country concluded a treaty over 200 years ago, just don't look at it too closely?
In all, I admire BO's optimism. I'm also not sure if anyone has a better chance of bringing about this vision of world peace than he does. I just don't think it's really possible, that's all.