The lighting of candles (votive lights) is accompanied by prayer. The fire represents the prayer with which the candle was lit. It's as if the fire prolongs the prayer after the person has left. The offering helps to pay for new candles when the old ones have burned down. Your father's handkerchief may have been to observe the old custom of women covering their heads when in church (Men removed their hats.) In any church with votive lights, you can light a candle whenever you visit, saying a prayer and making the suggested offering.
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