Eliot is talking about a classic process in chemistry called Catalysis. He pretty much explains what he means right there in the essay (read it at Bartleby's) but for more go to the wikipedia explanation of catalysis.
Basically, the platinum does something during the process that perhaps remains somewhat mysterious. I have not read up on the current level of understanding of this reaction in the literature, but certainly in 1922 when Eliot wrote the essay catalytic processes were not well understood. Even today they frequently remain very mysterious. But what they do, as Eliot says, is to assist in the reaction. That is, the catalyst lowers the initial energies required for the reaction to proceed. One chemistry text claims that the platinum acts as a surface catalyst. That is: it provides lovely surfaces where the oxygen and sulfur dioxide molecules can sit near each other in an orientation that favours a lower energy for their reaction. Maybe this is due to the surface crystalline lattice structure of platinum metal. I'm not sure. Maybe nobody knows. Perhaps it has just the right dimensions to make the oxygen and sulfur dioxide molecules happy. Since the catalyst is not actually involved in the reaction -- except perhaps in some very fleeting intermediate state that lasts only a millionth of second, it is not "counted" in the formula. Hence the chemistry can be described by the following formula:
2 SO2 + O2 → 2 SO3 (in presence of platinum)
What Eliot says is totally true. I suppose in his opinion, it is the ultimate goal of the artist to be a catalyst; to take his/her sense of the world and history and to create art that communicates feelings and emotions and ideas in such a way that the reader/viewer/listener actually has no sense of that artist. That is, like the platinum, the artist is not involved in the experience. Perhaps it's like when you see a great movie, or read a great book or poem, or enjoy a marvelous piece of music, you should be totally transported, you should be "right in the action" (the chemical reaction?) and you should have no thought of the artist who created it. You should be in the moment experiencing emotions and feelings so intensely that you are not aware of anything else, and certainly not that your experience was all "catalyzed" by some artist. While you are on the edge of your seat in a great thriller, or crying while reading a marvelous novel, you should not be thinking, "boy can this guy ever write." That would ruin the effect. A great artist is a perfect catalyst who neither takes from nor adds anything to the mix, so that the experience feels completely untainted by a third party. I guess Eliot is saying that the best artists ought leave nothing of themselves to get in the way of the experience of their art. Note that the artist as catalyst also must remain unaffected as well. Perhaps Eliot means that great artists are never proud of what they do. These are lofty goals indeed, achieved by very few.
I also get the feeling that Elliot suggests a fundamental creative source is playing a part in the poetic process - for which the poetic mind is catalyst. He refers to a metaphysical theory - substantial unity of the soul - which is separate from 'personality'. While I am not religious, and he certainly was, there must be some energy contained in culture, here poetic culture, that flows through time and history and expresses itself through individual poets. Of course there is also distorting dogma inserted onto this energy by personality and ego, so he differentiates and 'struggles', in his own words, to define the pure creative source.