When this root first appeared in The Etymologies (Ety/PHAY), it was glossed “radiate, send out rays of light” and its derivatives were consistent with this definition, most notably in N. Feanor “Radiant Sun”. In later writings, this root was instead glossed “spirit” (PM/352), which is the connotation of most of its later derivatives. For example, the later meaning of S. Fëanor was changed to “Spirit of Fire”.
The earlier sense “radiate” probably also survived in Tolkien’s later conception, however. On MR/250, the word Q. fairë “spirit” is said to originally have had the sense “radiance”, which is precisely the meaning that ᴹQ. faire had in The Etymologies. There is also a primitive monosyllable ✶phāy “flame, ray of light” in the Outline of Phonology from the early 1950s (OP2: PE19/102). If the root meaning “radiate” remains valid, then the word S. ✱fael “gleam of the sun”, an element of S. Faelivrin “gleam of the sun on the pools of Ivrin” (the second name of Finduilas), might be a derivative of this root.
The most notable function of this root was as the basis for the Quenya genitive suffix -o. The introduction of this root seems to predate the later iteration of this form of the Quenya genitive, with the root first appearing in The Etymologies of the 1930s as ᴹ√ƷŌ̆ where it served as the basis for the prepositions ᴹQ. ho/N. o “from” as well as an “old partitive” ᴹQ. -on (Ety/ƷŌ̆). In 1930s the usual Quenya genitive suffix was ᴹQ. -(e)n as in ᴹQ. Nyarna Valinóren “Annals of Valinor” (LR/202). However, the genitive suffix was often -o in earlier iterations of Quenya, and even in the 1930s it was a feature of the genitive plural, as in ᴹQ. ar antaróta mannar Valion “and he gave it into the hands of the Lords (Vali-on)” (LR/72).
After the conceptual shift of the primitive velar spirant from ʒ to h, this root became √HO (WJ/361), and Tolkien discussed its function at length in the Quendi and Eldar essay of 1959-60. He said it “was evidently an ancient adverbial element, occurring principally as a proclitic or enclitic: proclitic, as a prefix to verb stems; and enclitic, as attached to noun stems” (WJ/368). As proclitic it formed the verbal prefix Q. hó- “away, from, from among”, as an enclitic it formed the basis of the noun inflectional suffix -o used for genitives in Quenya of the 1950s and 60s. Its role in Sindarin is less clear, given Tolkien’s later vacillations on whether or not suffixal genitives were even a part of Sindarin.