O'Neill was a cop in Chicago who collected a rake of tunes with one of his colleagues and put them all down in a book. I suspect that he may be the same O'Neill who was helpful to Emma Goldman when she had some trouble in Chicago* but I'm not certain of it**. In any case, his collection has been, if anything can be, the standard collection of Irish dance tunes since it was set down. Krassen's edition of 1976 is a slightly different set of tunes with Krassen's suggested ornaments for fiddle, which are interesting but by no means definitive.
What does it mean to be "the standard collection" in this case? It does not mean that any given tune in this book will be known to any particular player. Most of them are quite forgotten by most players, in fact. It also does not mean that any given tune you hear in a session will be in this book. The Irish tradtition is a living one, and this partial collection gathered a hundred years ago represents only a small piece of what's out there today. What it does mean is that the tunes in this book, if you can play them tolerably well, will sound a little familiar to anyone who plays the music, and they'll probably have heard them, or something like them, somewhere before. And that's a pretty good trick for a collection of tunes.
It should be noted that the collection is skewed towards a very particular branch of the tune corpus, that being the tunes which are most amenable to western rules of harmony. That is, tunes with very clear harmonic structures are favored over those with the more ambiguous or outright contrary movement common to the tradition. This may reflect the tastes of Chicago in O'Neill's time, or O'Neill's personal taste, or a bias in transcription, or some combination of these, but it is worth noting that not all Irish tunes are harmonically so neat and simple as this collection implies. In that sense, this is a good starter kit: lots of good tunes to learn, but you have to get past it to get to a lot of the really good stuff. Some examples of the good stuff can be found in Breathnach's wonderful Ceol Rince collections, which are full of weird and great tunes that nobody plays, and some can be found in the tunes of Ed Reavy, one of the great composers of tunes, but the best place to look for the real thing is at your local session.
*see Goldman's autobiography for her version of the story
** I have since confirmed this story. ( )

This is the definitive handbook for learning Irish tunes and playing in sessions, whatever instrument you play. I'm a tin whistler myself and get a lot of value out of this book. ( )