An “intensive” root addition described by Tolkien in The Etymologies from the 1930s (EtyAC/A). It was one of two basic intensive mechanisms, along with the (syllabic) prefixed N- (EtyAC/N). The prefixed vowel a- seems to have been used originally in Primitive Elvish when the base vowel was a, and similarly with E and I (EtyAC/E; Ety/I²); whether this was also true of the vowels o, u is unclear, as Tolkien didn’t mention them. These various vocalic intensifications were frequently accompanied by dynamic lengthening (doubling), with the example given by Tolkien being: ᴹ✶parkā “dry” → ᴹ✶apparkā “very dry, arid” (> N. afarch).
In the case of e- and i-, the examples were dero, dise → ᴹ✶Endero, ᴹ✶Indise “groom, bride”; these examples indicate that other kinds of consonant fortifications were possible, in this case nasalization of stops, which often replaced consonant-doubling for voiced stops in Primitive Elvish.
Specifically in the case of a-, however, it seems it could be used as a general intensive that “was distinct in origin, though similar in function, to the prefixed basic vowel”. Why this was true of a- alone is not clear, but there seems to have been some complex interplay between the vocalic intensives and the intensives derived from syllabic initial ṇ-, with the net result that the intensive prefix in Q. became an-, am-, añ-, depending on the initial consonant.
See the entry on the Quenya comparative for a more detailed discussion of the conceptual development of intensives in Eldarin.