The appeal of socialism was the fact that it promised to give working people a greater share in the prosperity that was being created in the United States during this time.
The late 1800s and early 1900s were a time in which the US economy was booming. The factories that sprang up and expanded were filled with unskilled laborers working for low pay in poor conditions. This was highlighted by, for example, the Triangle Shirtwaist Company Fire.
In this environment, socialism would seem very appealing. Socialism promised to take power away from the rich and give it to the workers. It promised to give the workers political power as well as power over the economy. By doing this, it would make workers equal to those who currently dominated them economically and politically. These promises were very appealing to a class of working people who felt oppressed during this time.