In my travels around various churches, I often see one of these stands with votive candles somewhere in the narthex or back of the nave.... a place to light candles to signify the intention to say a prayer for someone. They come in all sizes and shapes (at the San Carlos Borromeo Mission in Carmel, California, there was a lovely display of very thin beeswax candles standing in a small tub filled with sand just off to the left of the altar rail in the nave) and there is often a spot (a slot, a basket) in which money can be placed - not as a bribe related to the prayer but an offering to defray the cost of the actual candles.
One of the churches I have had a relationship with began opening its doors in the daytime to the public and discovering that people were coming in off the street and lighting candles. This was, fortunately, seen as a positive thing, that the church was a place in which people came inside to pray and they left evidence of those prayers by lighting candles.
I wonder why it is that we feel the need to leave evidence of our prayers or do make a physical act out of it. I myself light candles, and I don't think it's a silly practice at all; in fact, I believe such practices go back into time immemorial. People leave signs. In the Old Testament piles of stones were used as memorials to the miracles of YHWH. (See Genesis 31:46; Joshua 4:3-20 for example.) Graffiti is another way. (Kilroy was here.) We want to do something that signifies our thoughts, our feelings, our intentions, our memories.
Even people who don't consider themselves particularly religious will, when they find themselves in a church, say on a tour or something, and they see one of these set ups, will come over and light a candle.
I believe that this practice is a way of offering a light against the darkness.