Why do we light candles on Rosh Hashanah?
The candles of Rosh Hashanah are similar to those of other holidays, and to those of Sahbbos.
For the rationale behind lighting candles, please see below.
Two principle reasons are suggested as the purpose of the Shabbos candles. In one place (Shabbos 25b), Rashi explains that the purpose of the Shabbos candles is for the honor of Shabbos, for a meal can only be considered ‘honorable’ if eaten in a well-lit place.
The Rambam, moreover, writes explicitly (Shabbos 5:1) that “the candle must be lit, the table laid, and the bed made, for all these involve the honor of the Shabbos.” The Yere’im (429) likewise states that the lights must be kindled in honor of the Shabbos.
Yet, elsewhere (5:1) the Rambam writes that the purpose of the Shabbos candles is for the ‘delight’ (oneg) of the Shabbos, meaning in order that one should be able to enjoy the day (or, rather, the night). The Shulchan Aruch Ha-Rav (263) opens the section on Shabbos candles by explaining that their purpose is to provide lighting, allowing people to feel comfortable and guarding them from obstacles.
In a similar sense, the Gemara (Shabbos 23b) writes that the purpose of the Shabbos candles is for Shalom Bayis (harmony of the home), Rashi explaining that “the household are distressed to walk in the dark.” The Aruch Ha-Shulchan (263:2) explains that the concept of shalom bayis is included in the ‘delight’ of the Shabbos.
It is noteworthy that in order to fulfill the concept of shalom bayis with the Shabbos candles, one should insure that there is some illumination in every area of the home that will be used on Shabbos, so that everyone will be able to find their way around without any discomfort.
Because of the numerous sources pointing at both rationales, the halachah follows both, and by lighting Shabbos candles one fulfills both the mitzvah of honoring the Shabbos, and the mitzvah of ‘delight’ on Shabbos.