Learn Italian: D'accordo, va bene!

It stands for the word di (which usually means "of" or "from"). When di comes right before a word starting with a vowel, like accordo, the letter "i" is dropped and replaced with an apostrophe to make it flow better. So, it literally means "of agreement".

Why do we say va bene for "all right"? What does it literally mean?

Va is the "it" form of the verb andare (to go), and bene means "well". So, va bene literally translates to "it goes well". Italians use this exact phrase all the time to mean "okay", "all right", or "that works".

Are d'accordo and va bene just two ways of saying the exact same thing?

They are very close, but have a slight difference. D'accordo specifically means you agree with someone (like saying "agreed!"). Va bene is a more general "okay" or "that's fine". Using them together in one breath, as seen here, is a very common, enthusiastic way to say "Okay, I agree!"