Lighting candles before Shabbat begins is a Rabbinical, not a Biblical commandment. The Rabbis saw that many times, people would forget to leave the lights (=in those days, candles) on before Shabbat began and when they would come home from the Synagogue they were forced to have Shabbat dinner in total darkness, which (i) generated tensions between husband and wife and (ii) it diminished the honor and enjoyment of Shabbat.
They established then, that it should be mandatory to light the candles before Shabbat begins. In this way, this candle-lighting would avoid a disruption of the peace and harmony between husband and wife or other members of the family (Shalom Bayit) and it created an environment with more light, thus increasing the honor and enjoyment ('oneg) of Shabbat.
Shabbat candle-lighting is not a personal or individual Miṣva , but a family (or a household) Miṣva. Quoting Maimonides (MT, Shabbat 5:1) "Men and women, they have to have in their homes a candle lit on Shabbat".
Normally it is the woman who is primarily in charge of lighting the candles (the tradition is that men also should be part of this Miṣva by preparing the candles, placing them in the candle- holders, pamotim, etc.) If the woman of the house is not home, or if she is not able to light the candles, then the husband or any adult member of the family should light the candles, and recite the corresponding blessing.
According to Sephardic tradition there is no obligation for the single daughters to light additional candles. However, if they still want to light candles (to be trained or educated in this Miṣva) they could do so, provided they do not recite the blessing for those candles, because, as we explained, Shabbat candle lighting is not a personal obligation, but an obligation for each house.
Candle lighting in NYC: 4:23 p.m.
Shabbat Ends in NYC: 5:21 p.m.