Theory:

     Christmas Eve had arrived. As last-minute shoppers were going home, a thick, white sheet of snow lay over Salt Lake City, USA. Yet the lights were still burning in the old-clock shop, as Ray, its old, deaf owner, worked on a clock he had sold that day.
Explanation:
 
The story takes place during the Christmas Eve. Joy and spirit that come with Christmas were spreading everywhere. And so was the snow. Salt Lake City, where the story was taking place, was covered with snow.
 
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Christmas Eve
 
While it is common to have snow during the Christmas season, snow can also be seen as a metaphor.
 
Snow is a sign of hope and a new beginning. As Shelly had said, "if winter comes, can spring be far behind?" Yet, it can also symbolise hardships and gloominess.

While winter and snow are aesthetically pleasing, freezing weather can be hard on the poor. They may not have proper shelter to protect themselves from the cold. Hence, snow can be a symbol of beauty and pain.

Moreover, the story describes the snow as ‘a thick, white sheet lying over Salt Lake City’.
 
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*Map of USA (highlighting Salt Lake City in the state of Utah)
 
The snow is thick, and hence it means that it is severe. Moreover, it was lying over the city, as though the city was being hidden from the heaven's eyes. The line suggests that various forms of evil are lurking around, yet humans are all by themselves to deal with it.
 
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A thick, white sheet of snow lay over Salt Lake City

Furthermore, it is essential to note that people tend to become more desperate during the festival season. For instance, during Christmas (or any festival for that matter), some celebrate, and some cannot afford a celebration. Imagine how the less fortunate people might feel when they have no means to celebrate? Especially when they see the others celebrating while they cannot give their family a decent meal. These are the times when even the innocent people are pushed into the wrong paths, out of their desperate need to live a normal life.
 
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A homeless man

Back to the story, we see that the day has come to an end, paving the way to the Christmas Eve. People were going back to their homes after their last-minute shopping. Most of the shops were closed for the day. The shopkeepers were also probably rushing back home to be with their family and friends.
 
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The last-minute shoppers were going home
 
However, an old-clock shop remained open. Ray, an old deaf man, ran it. The day the story took place, Ray had been working on a clock which he eventually sold.
 
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Ray worked on a clock he had sold that day

The line "yet the lights were still burning in the old-clock shop" may have an undertone. While the idea of 'burning lights' may simply mean that the shop was open, it can also be seen as a metaphor. "Light" can be seen as a symbol of hope.
 
While the city lay covered in snow and the day gave way for the night, the light from the clock shop spread brightness around. Or to be metaphorical, while poverty and the human sufferings were increasing, hope was still to be found in the heart of Ray. As you delve deeper, the name Ray itself is symbolical as it denotes 'light' and can be seen as a ray of hope.
 
Meaning of difficult word:
 
S.No
Words
Meanings
1
Christmas Eve The evening or entire day before Christmas Day
Reference:
National Council of Educational Research and Training (2006). The Old-Clock Shop (pp. 11-14). Published at the Publication Division by the Secretary, National Council of Educational Research and Training, Sri Aurobindo Marg, New Delhi.
 
*PC: https://commons.wikimedia.org/wiki/File:Map_of_USA_showing_state_names.png