The lighting of Shabbat candles in the home is a ritual steeped in symbolism.
According to the Torah, Shabbat itself is a reminder of the creation, and the kindling of lights is, in this context, seen as reminiscent of God’s creation of the first light. On a day in which traditionally observant Jews sometimes refrain from using electric lights, the Shabbat candles also bring warmth and illumination to an otherwise darkened home.
But there is another tradition that candle lighting is a symbolic rectification for Eve’s sin of eating from the Tree of Knowledge in the Garden of Eden. The source for this has its root in the Midrash, which describes how the sin of Eve removed a little bit of light from the world. Lighting the Shabbat candles is our way of putting that light back into the world.
The Jewish legal work known as the Tur cites the custom: Tur Orach Chaim 263
והנשים מוזהרות בו יותר כדאיתא במדרש מפני שכבתה נרו של עולם פירוש גרמה מיתה לאדם הראשון והרמב”ם ז”ל נתן טעם לדבר מפני שמצויות בבית ועוסקות בצרכי הבית
[Both men and women are commanded to light,] but women are more commanded than men, as it says in the Midrash: Since she extinguished the lamp of the world, meaning she caused the death of the first human. And the Rambam explains [that women are more obligated] because they are found at home and they take care of household needs.
Here is the original source in the Midrash: Bereishit Rabbah 17:8
ומפני מה ניתן לה מצות חלה? על ידי שקלקלה את אדם הראשון, שהיה גמר חלתו של עולם, לפיכך ניתן לה מצות חלה. ומפני מה ניתן לה מצות נר שבת? אמר להן: על ידי שכבתה נשמתו של אדם הראשון. לפיכך, ניתן לה מצות נר שבת.
And why was she [Even, woman] given the commandment of challah? Because she disgraced the first man, who was the sanctification [challah] of creation, therefore she was given the commandment of challah. And why was woman given the commandment of lighting Shabbat candles? He [God] said to them: because she put out the soul of the first man, therefore she was given the commandment of Shabbat candles.