The source in the Mishnah – we already find the matter of lighting a candle in honor of the dead in the Mishnah, אֵין מְבָרְכִין …, וְלֹא עַל הַנֵּר וְלֹא עַל הַבְּשָׂמִים שֶׁל מֵתִים, (ברכות פ”ח מ”ו) and in the Gemara אֵין מְבָרְכִין …, וְלֹא עַל הַנֵּר וְלֹא עַל הַבְּשָׂמִים שֶׁל מֵתִים: מאי טעמא נר לכבוד הוא דעבידא. (ברכות נג,א)

At the time of the Tannaim – already by the time of the Tannaim, the Jews of Eretz Israel had the idea that the dead also need forgiveness. The Sifre is learning on the Pasuk in the Torah: כַּפֵּר לְעַמְּךָ יִשְׂרָאֵל אֲשֶׁר פָּדִיתָ ה’ (דברים כ”א,ח), כַּפֵּר לְעַמְּךָ יִשְׂרָאֵל – these are the living, אֲשֶׁר פָּדִיתָ – these are the dead, so we see that the living are releasing the dead, that is why we usually remember the dead on Yom Kippur and give for them Zdaka.

A soul is called a candle – Regarding this custom, it was probably customary in the Middle Ages, that everyone lights a candle to atone for their deceased father and mother. (דרכי משה לטור או”ח, תר”י) This custom has continued to our day’s, and one of the last Poskim justifies it as follows: וזהו תיקון הנשמה, דנשמה מקרי נר, כדכתיב: נֵר ה’ נִשְׁמַת אָדָם (משלי כ,כז), וגם המתים צריכים כפרה כדאיתא בספרי (ערוך השולחן או”ח תר”י,).

The time and place of lighting – it is customary to light a candle in honor of the deceased and to raise his soul (called a soul candle / memorial candle) in his home, or in the house of mourning, from the time of death until the end of the seven days (“the Shiva”), and on the anniversary of his death (as well as during grave visits). In previous generations there were communities that used to light a candle during the twelve months in the synagogues.

The type of candle – some people are lighting an olive oil candle, and some people are lighting a wax candle, if it is not possible – a normal candle is lit, and as in every Mitzvah, you can appoint a messenger.

The soul enjoys the lighting of the candle – the Rabbeinu Bachya explained: the soul enjoys the lighting of the candles and it walks in the refinements of majesty and joy, and spreads and expands out of the pleasure of the light because it is a piece of light carved in the light of the mind, and for this reason it is drawn to the light that he appointed even though it is a physical light and the soul is a spiritual light, and that is why Shlomo compared the soul, like he sayed: נֵר ה’ נִשְׁמַת אָדָם. (משלי כ,כז) (רבינו בחיי שמות כה,לא)