Theory:

     At last, Soapy came to one of the quiet streets on the side of the city. He turned here and began to walk south toward Madison Square. He was going home, although home was only a seat in a park.

     But at a very quiet corner, Soapy stopped. Here was his old childhood home. Through one window, he could see a soft light shining. That had been his living room, where he had spent many happy peaceful moments. Sweet music came to Soapy’s ears and seemed to hold him there.
Explanation:
 
After trying hard to get caught by the policeman, Soapy's various plans got failed. Finally, he reached one of the quiet streets on the side of the city. He decided to walk south towards Madison Square. He planned many tricks to get caught by the police, but he failed in every attempt. So in sadness, Soapy thought of going home. As everyone knew, Soapy was a homeless and jobless man. But here, he was going "home" meant that he was going back to Madison Square park. According to him, "a seat in the park" was only his home.

Soapy stopped walking while he saw a quiet corner. 'There he saw an old church. It was his childhood home'.* He could see a soft light shining out through one of the windows. The room where light peeped out was his older room. At the same time, while seeing that, Soapy recalled the happy times he had spent in his childhood home. At that moment, Soapy heard a sweet music coming out through the window and it made him stop there.
 
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Soapy stopped in front of an old church (childhood home)
 
Meanings of the difficult words:
 
S.No
Words
Meanings
1
WindowAn opening in the wall or roof of a building or vehicle, fitted with glass in a frame to admit light or air and allow people to see out
2
ShiningGiving out or reflecting bright light
3
Living roomA room in a house for general everyday use
4
Peaceful Free from disturbance; tranquil
5
MomentA very brief period of time
Reference:
National Council of Educational Research and Training (2007). An Alien Hand. The Cop and the Anthem- O. Henry(20-29). Published at the Publication Division by the Secretary, National Council of Educational Research and Training, Sri Aurobindo Marg, New Delhi.