I understand that the amino acids in living oranisms are left handed, but what is the functional difference between left handed and right handed amino acids and what function do right handed amino acids serve?
The D-amino acids are biologically inactive, except in a few lifeforms and bacteria evolved to use them instead of the L-amino acids. That’s all it is. Full stop. D-amino acids get some use as chiral precursors, but they’re more expensive than the natural L-amino acids.
I guess I didn’t really answer the first question. Think of the stereochemistry as trying to cram a right-handed glove on your left hand. It won’t work. Similarly, all biochemical processes will simply not work with a D-amino acid because it just won’t fit the highly specific sites. This is true for all stereochemical molecules in a living system, not just the amino acids.
Anyway, we often have to synthesize D-amino acids instead of being to isolate them from natural sources. That’s why, as I said about the precursors, they’re more expensive.
This needs a little clarification. There aren’t any life forms that use exclusively D-amino acids to make their proteins etc. However many bacteria as well as other organisms incorporate D-residues into proteins by post-translational modification of existing L-residues.
D-amino acids also occur as essential parts in many antibiotic peptides.
Oh yes, one reason for incorporating D-amino acids into peptides is that the mirrored residues often slow down the rate at which a cell’s proteases can degrade the structure.
In the case of an antibiotic, that means that the target organism has a harder time eliminating the D-based toxin than it would an L-based analog.
Eh, I’m just an organic chemist. Stereochemistry is important, but I’m not used to thinking of biochemistry, unless I’m reading about a total synthesis or something.
But am I at least close enough for a general understanding?
Yeah, for a chemist. 
When it comes down to a reaction at a protein’s core, stereochemistry rules, beyond that, biochemical catalysts are ugly, squishy, wiggly things.
But they have great personalities!
Do all lifeforms use left-handed amino acids simply because that’s what our common ancestor used, or is there something inherent in left-handed amino acids that makes them more suitable for use by living things?
Current thinking is the former. There’s no real benefit of one over the other, so it seems that the first blob of goo to make these things happened to make one kind instead of the other kind, and we’ve all done it that way since.
Exactly. They’re chemically identical except for the stereochemistry.
Why do we drive on the right side of the road?
Because that’s how we started and that’s how it’s always been done. Similarly advanced systems using the exact oposite orientation have similarly evolved using the exact opposite.
The book “Right Hand, Left Hand” by Chris McManus deals in part with your question, although it also goes into broader topics. It’s a great book, I highly recommend it.