Named after the preferred use of such a comma to avoid ambiguity in the house style of Oxford University Press, Oxford comma denotes a comma immediately preceding the conjunction in a list of items.

The following explanations are from The Guardian and Observer style guide, edited by David Marsh and Amelia Hodsdon:

Oxford comma
a comma before the final “and” in lists: straightforward ones (he ate ham, eggs and chips) do not need one, but sometimes it can help the reader (he ate cereal, kippers, bacon, eggs, toast and marmalade, and tea).
Sometimes it is essential: compare
I dedicate this book to my parents, Martin Amis ¹, and JK Rowling ²
with
I dedicate this book to my parents, Martin Amis and JK Rowling

¹ Martin Louis Amis (born 1949) is a British novelist.
² Joanne Kathleen Rowling (born 1965) is a British novelist.

The first recorded uses of Oxford comma are from The Oxford University Press: An Informal History (Oxford University Press, 1978), by Peter Sutcliffe:

1-: In the following passage, Peter Sutcliffe writes about Authors’ and Printers’ Dictionary, by the British printer, indexer and editor Frederick Howard Collins (1857-1910):

It was Collins who invented the ‘Oxford comma’, for which he obtained support from Herbert Spencer ³. In his entry ‘“and” or, “, and”’ ⁴, he quoted Spencer’s verdict on whether to write ‘black, white, and green’, with the comma after white: ‘inasmuch as when enumerating these colours . . . the white is just as much to be emphasized as the other two, it needs the pause after it just as much as the black does.’

³ Herbert Spencer (1820-1903) was a British philosopher and sociologist.

⁴ The entry “and” or, “, and” mentioned by Peter Sutcliffe is as follows in Author & Printer: A Guide for Authors, Editors, Printers, Correctors of the Press, Compositors, and Typists. With full list of Abbreviations. An Attempt to codify the best Typographical Practices of the Present Day (Oxford: Horace Hart Printer to the University – Published by Henry Frowde – 1905):

“and” or, “, and” The late Herbert Spencer allowed me to quote from his letter:—“whether to write ‘black, white, and green’, with the comma after white, or to leave out the comma and write ‘black, white and green’—I very positively decide in favour of the first. To me the comma is of value as marking out the component elements of a thought, and where any set of components of a thought are of equal value, they should be punctuated in printing and in speech equally. Evidently therefore in this case, inasmuch as when enumerating these colours black, white, and green, the white is just as much to be emphasized as the other two, it needs the pause after it just as much as the black does.”

2-: Peter Sutcliffe uses Oxford comma again in the following passage about the publication of A School History of England (Oxford: Clarendon Press, 1911), by the British novelist, short-story writer and poet Rudyard Kipling (1865-1936) and the British historian Charles Robert Leslie Fletcher (1857-1934):

The printer’s reader had been punctuating Kipling’s verses as he had Fletcher’s prose, introducing amongst other things the Oxford comma. Fletcher could not abide it. ‘May your reader who inserts commas where I had specially left them out (e.g. Lancashire, Devon, and Cornwall) be fried alive,’ he wrote in his usual robust vein to Cannan ⁵, ‘with the author of the “King’s English” told off to keep him from dying too quick.’ Kipling, though he did not approve, was more accommodating. ‘I abhor an abundance of commas but if it’s the Clarendon Use put em in. I think it makes the sentences sloppy.’ An interesting problem for the textual critic.

⁵ Charles Cannan (1858-1919) was Secretary to the Delegates (i.e., Chief Executive) of the Oxford University Press from 1898 to 1919.

The earliest occurrences of Oxford comma that I have found are from L. M. Boyd’s trivia column, published in many U.S. newspapers on Friday 9^th November 1990—for example, in The Post-Star (Glens Falls, New York):

Serial comma
Q. What’s a “serial comma”?
A. A comma to separate items in a series. As in: “a, b and c.” Do you know what an “Oxford comma” is? One that precedes a conjunction. As the one between the “b” and the “and” in: “a, b, and c.” Hardly anybody uses the Oxford comma anymore. It’s rarely needed.

The second-earliest occurrences of Oxford comma that I have found are from a trivia quiz in Curiosity Corner, by Dr. Jerry Wilson, Emeritus Professor of Physics, Lander University—published in The Index-Journal (Greenwood, South Carolina) of Sunday 1^st June 2003:

What is a “Harvard” or “Oxford” comma?
Here’s your English lesson for the day. A Harvard or Oxford comma refers to the “serial” comma in a list before the “and.” For example, “You have a choice of ham, bacon, and sausage.” This can be also written: “You have a choice of ham, bacon and sausage.” (Without the Harvard comma.) The latter sentence could cause confusion. It might be interpreted that you could have a choice of (1) ham, or (2) bacon and sausage (both?). Harvard and Oxford University Presses use the “serial” comma, hence the name.
However, it is sometimes omitted to save space. I hope the typesetter doesn’t leave it out here.

On Sunday 26^th January 2020, the British author Philip Pullman (born 1946) declared this on the social media application Twitter:

The ‘Brexit’ 50p coin is missing an Oxford comma, and should be boycotted by all literate people.

He was referring to the following inscription on the Withdrawal from the European Union 2020 UK 50p Coin—photograph The Royal Mint:

Peace, prosperity and friendship with all nations