The quote comes from C. K. Scott Moncrieff's translation of Swann's Way. Below is a longer quote from the paragraph in the original French (as available on Wikisource), in which I have highlighted a few phrases:
Elle ne parlait jamais qu’assez bas parce qu’elle croyait avoir dans la tête quelque chose de cassé et de flottant qu’elle eût déplacé en parlant trop fort, mais elle ne restait jamais longtemps, même seule, sans dire quelque chose, parce qu’elle croyait que c’était salutaire pour sa gorge et qu’en empêchant le sang de s’y arrêter, cela rendrait moins fréquents les étouffements et les angoisses dont elle souffrait ; puis, dans l’inertie absolue où elle vivait, elle prêtait à ses moindres sensations une importance extraordinaire ; elle les douait d’une motilité qui lui rendait difficile de les garder pour elle, et à défaut de confident à qui les communiquer, elle se les annonçait à elle-même, en un perpétuel monologue qui était sa seule forme d’activité.
Below is C. K. Scott Moncrieff's translation of the same excerpt, with the corresponding phrases highlighted:
She never spoke save in low tones, because she believed that there was something broken in her head and floating loose there, which she might displace by talking too loud; but she never remained for long, even when alone, without saying something, because she believed that it was good for her throat, and that by keeping the blood there in circulation it would make less frequent the chokings and other pains to which she was liable; besides, in the life of complete inertia which she led she attached to the least of her sensations an extraordinary importance, endowed them with a Protean ubiquity which made it difficult for her to keep them secret, and, failing a confidant to whom she might communicate them, she used to promulgate them to herself in an unceasing monologue which was her sole form of activity.
In this excerpt, Proust uses several phrases and images that refer to either movement and activity and their opposites, inertia and passivity. Where C. K. Scott Moncrieff wrote "Protean ubiquity", Proust had written "motilité", which, as the French Wikpedia explains, is
un terme de la biologie qui réfère à la capacité de se déplacer spontanément ou par réaction à des stimuli et activement, en consommant de l'énergie lors du processus.
In other words: a term from biology that refers to the ability to move around spontaneously or as a reaction to stimuli and actively, while consuming energy during that process.
The adjective "Protean" derives from the name of the Greek god Proteus, who was capable of changing shape. Something endowed with "Protean ubiquity" would presumably be able to be "everywhere" as easily as Proteus changes shape. However, "motilité" implies neither shapeshifting, nor omnipresence, so by translating "motilité" as "Protean ubiquity", C. K. Scott Moncrieff breaks the chain of phrases and images that refer to movement or inertia.