(covers information from several alternate timelines)
An accent was a vocal inflection particular to the people in a specific geographical region.
In 2152, a Risan woman told Hoshi Sato that she spoke the Risan language with hardly any accent. (ENT: "Two Days and Two Nights") Feezal Phlox also noticed the same thing when Sato spoke Denobulan. (ENT: "Stigma")
In both the prime reality and the alternate reality, Pavel Chekov's Russian accent caused him to pronounce "V"s as "W"s and vice versa. A passerby had difficulty understanding Chekov who was looking for "nuclear wessels" in Alameda. (Star Trek IV: The Voyage Home) The computer of the alternate reality USS Enterprise could not entirely distinguish between accented speech and a mistake in a spoken authorization code, much to Pavel Chekov's frustration. It required several tries for him to pronounce the code distinctly enough for the computer to recognize it and allow him access. (Star Trek)
In 2369, multiple holographic characters from an Ancient West holoprogram (which, due to a computer glitch, took on the appearance of Data) exhibited different accents, including Western and Mexican. (TNG: "A Fistful of Datas")
In 2374, Vic Fontaine removed the Russian accent from Julian Bashir's holographic character Lola Chrystal – a feat which took over an hour – to allow Odo to pretend she was Kira Nerys. (DS9: "His Way")