The custom of lighting two candles on Shabbat signifies the two aspects of the mitzvah given in the Torah. Deuteronomy 5:12 tells us to "Observe (shamor) the Shabbat day and make it holy." Exodus 20:8 instructs us to "Remember (zachor) the Shabbat day and make it holy."
The Talmud explains that at Mt. Sinai, at the giving of the Ten Commandments, G-d caused the people of Israel to hear both of these terms at the same time in a single utterance (Shavuot 20b).
In this regard it is a custom in most communities to sing "Lecha Dodi" each Friday night as part of the Kabbalat Shabbat service which welcomes the Shabbat.
The second stanza reads: "Shamor v'zachor b'dibur echad...." - "'Observe' and 'remember' in a single utterance...."
Actually, the mitzvah of lighting candles for Shabbat can be accomplished with only one candle (Mishnah Berurah 263:6)
However, it is a beautiful custom to light two or even more candles in honor of Shabbat.
In the words of our sages: "A little light dispels a lot of darkness."