This is a great question! It is a real shame that some threads of doubtful usefulness (Yundi Li x Lang Lang; overrated pianists; underrated pianists; etc.) get hundreds of replies, and interesting and useful ones like this one will probably die pretty soon.
Although I agree with xvimbi to a certain extent that “taste” is necessary (I would say “good taste” though), I am not convinced at all that it is sufficient, or even the most important factor. For a start, who is going to be the arbiter of taste? I tend to regard music like I regard chess. Certainly it is a beautiful, elegant and aesthetically pleasing game, but taste, is hardly the criterion by which one would judge a game, although certainly the best games will have this component in it as well.
Here are some more thoughts on this matter:
1. Baroque ornamentation was left to the performer. The composer often just gave the melodic and harmonic skeleton of the piece and it was up to the performer to freely improvise ornamentation. It was not just a matter of trills, mordents and appoggiaturas, but actually creating a “melodic” line whenever an opportunity arose. So it was very common if the composer’s melody, say, went from C to G, for the performer to play C – d – e – f – G, that is insert a stepwise progression between two distant notes. This was a living tradition, that is, it was not learned in books, but passed from master to pupil, very much like Jazz improvisation. Unfortunately such living tradition is now dead. We truly do not know how performers freely improvised ornaments. There are lots of conjectures, but the truth of the matter is that we don’t know. We are in the same situation as Egyptologists: we may have deciphered the hieroglyphs, but we have no idea how they were actually pronounced, nor will we ever know (short of a time machine, or if some mummy does come alive!

).
2. I learned a lot about free ornamentation from playing the Baroque repertory for the recorder, since in that instrument you are expected to freely ornament – much more than on the piano. So you may find a lot of useful information in recorder-related material (and also other historical instruments like the viola da gamba). Nevertheless, what I said in (1) still applies here. The recorder pretty much disappeared from the musical scene around 1750 (when it was replaced by the transverse flute). When it was rediscovered in the early 1900’s, the ignorance about it was such, that the performer put a piece of plaster on the thumbhole because they had no idea what its function was. Since then many old instruction manuals for the recorder (some dating as far as the 1500s) have been discovered and a number of lost techniques were rediscovered. To have a taste of the kind of ornamentation I am talking about here, I suggest you listen to this CD (if the freely improvised ornaments do not blow your mind, nothing will):
https://www.musicstrands.com/action/detailAlbum/albumId/412860As usual in Baroque times, slow movements were heavily ornamented: the first time the movement would be played more or less as written and on the repeat, all hell would break loose and the performer could give free rein to his imagination, but always
within rules. The problem of course is that such rules were for the most part unwritten and taken for granted.
A very interesting and illuminating book is:
Freda Dinn – “Early music for recorders: and introduction and guide to its interpretation and history for amateurs. (Schott)
[Amongst other works she does a step by step freely improvised ornamentation on Handel’s Sonata in G minor for recorder and continuo explaining why].
3. As the Baroque was coming to a close, many composers started resenting the liberties performers were taking in their free ornamentation, and most notably J. S. Bach, G. Handel and F. Couperin started writing their own ornaments on their compositions – a fact much resented by performers (“who do these composers think they are! The nerve of it, telling
us how to play the music!”). Both Couperin and Bach (through his son C.P.E.) wrote extensive instruction manuals on how they wanted their pieces ornamented. Of course – for all the valuable information they give us on ornamentation – this goes completely against the art of free ornamentation.
The editorial approach to ornamentation – more often than not – tends to take these instructions manuals as dogma.
4. So when you hear someone embellishing music contrary to respected editions directions, this maybe either because the performer is actually ignorant of them and just decided to follow his own “taste”, or it maybe because the performer has gone deeply into the Baroque mind and has come up with something that may actually approach an authentic ornamentation practice (although we can never be sure of that). Usually a bona fide performer will be able to explain his choice of ornamentation in a cogent manner, while an ignorant performer may babble something about “how good it all sounds”.
5. An extremely thought provoking reference (it provides no easy answers) on this and other matters is:
Nikolaus Harnoncourt: “Baroque music today – music as speech” (Amadeus Press).
6. Other fundamental references are:
Robert Donnington – “The interpretation of Early music” (Faber) – This is the standard reference book for performance practices in the Baroque.
(Donnington has several other interesting books – the one above is the basic one).
Frederick Neumann: “ Ornamentation in Baroque and Post-Baroque Music”
(Princeton)
[The ornamentation Bible].
Best wishes,
Bernhard.