Eliot's poem is an example of a style of writing called modernism, which was a reaction to many world events, and to previous styles of writing. Industrialization was the main force in the world, and wars were brewing. Many people were left questioning almost everything about existence, and feeling disconnected. Because of wars, and because of the hard, dirty, unglamorous lifestyle that industrialization brought, authors were left questioning previously held notions about goodness, writing styles, and relationships. So, the Modernist movement attempted to reflect the fragmented and shattered mind-frame of so many during that time period. They also shunned previous literary conventions. So, when Prufrock was released, it was something that was highly criticized because it was so different than anything that had come before it. Eliot used stream-of-consciousness writing to create a dream-like and wandering effect, in order to reflect more accurately how people really think. We follow Prufrock's mind as it journeys in and out of focus, all around his own insecurities; he feels alienated from the person he wants to speak to, and senses the futility of all of the daily, ridiculous routines that people cling to even in the face of larger issues. All of these things-the writing style, the alienation, the questioning of life-reflect the modernist movement. Eliot's poem was received with mixed reactions; professed critics tore it apart, saying that it was disjointed, confusing, and amateur. Others who were more in the modernist movement loved it. But it stemmed from that disillusionment with life, and with a need to present things as they really are in order to reflect reality, not to present them as people wished they would be. So, we get Prufrock and his wandering mind, even if it is rambling, because that is more like real human beings think.
I hope that those thoughts help a bit; I provided a link below that gives even more background information. Good luck!