The first part of the question is easy to answer. The Oxford comma, also known as the serial comma, is the final comma used in a series or list, together with "and" or "or". Therefore, a sentence with a correctly used Oxford comma would be:
"We studied the drug's effect on the subjects' appetites, sleep patterns, and length of life." The same sentence without the Oxford comma would be "We studied the drug's effect on the subjects' appetites, sleep patterns and length of life."
Here you're starting to think, "Okay, but what's the big deal? Both of those sentences mean exactly the same thing!" In this case, you're right - both of these sentences would be interpreted by most reasonable readers to mean the same thing. However, consider the following examples:
"We quantified the expression of the two new genes, Maj10, and Mak20."
"We quantified the expression of the two new genes, Maj10 and Mak20."
In the first example, the commas are used to identify individual items in a list, and the reader can see that we've quantified the expression of four genes: two new genes (presumably identified previously in the text), plus Maj10 and Mak20. However, it's not clear in the second example if "the two new genes, Maj10 and Mak20" makes up a list of four different genes, or whether the comma is used simply to set off additional information that describes the noun before it ("genes"). If the latter is true, we have only two genes, named Maj10 and Mak20. See the problem? If we chose not to use the Oxford comma in our writing, sentence #2 could describe either situation. Some readers may infer that we studied four genes, while other readers, expecting to see an Oxford comma in this situation, will infer that we studied only two genes. By contrast, sentence #1 is clearly a list of four genes.
Now that we know what it is, then, let's deal with the second half of the question: why does it cause such emotionally charged debates? For the sake of full disclosure, I should reveal that I am a proud member of Team Oxford Comma, for two reasons. First, because Mr. Stanich taught me to use it when I was 11, and when I asked him "Why?", he said "Because". Old habits die hard. The real reason, however, is that it eliminates confusion. If I use the Oxford comma correctly and consistently, my readers will have no difficulty in interpreting sentence #1 as a list of four genes and sentence #2 as an identification of two genes. They will reason, rightly so, that if I'd meant #2 to be a list of four genes, I would have put an Oxford comma in it. Instead, if I use the Oxford comma haphazardly, or not at all, sentence #2 will, at best, sidetrack my readers with unnecessary head-scratching, and, at worst, lead them down the exact opposite path from what I intended.
Most writers who advocate minimal usage of the Oxford comma are journalists, following AP style guidelines. When you think about it, this makes sense - writing for a newspaper requires packing as much information as possible into limited physical space, and taking out individual punctuation marks could make a difference. In academic publishing, however, the benefit (space for 10-15 extra characters) doesn't come close to outweighing the cost (imprecision and potential reader confusion). If you're trying to communicate a complex, involved research project to unknown readers, why handicap yourself? Team Oxford Comma for the gold!