The creature begins his tale in Chapter 11 of the novel, and his ability to speak eloquently makes all the difference in the world. Until this time in the book, we have only gotten Victor's point of view. We know the creature is huge, ugly, smiles strangely at Victor as the creature pulls back the bed curtains (indicating a certain malice or intention to do harm?), and faster than normal humans. He has been built up in the reader's mind to be some big, dumb, evil being that Victor should have never brought into the world for all the damage the creature will now wreak on humanity. However, his speech is convincing. He tells us how he came into being as a gentle soul, only looking for love and acceptance from his "father" and humanity. He tells us how he has been treated like Shrek...everywhere he went people screamed, "Grab your pitchforks!" and they chased him out of fear before ever getting to know him. He is abused, and rejected time and again. The De Lacey family was the last straw. At this point in his life, the creature vows revenge on his father who abandoned him to this fate. With all of this intelligent and articulate summary of his life, he then presents Victor with the purpose of his visit. He wants a companion--someone like himself, who won't cringe at the sight of him. Most readers agree at this time that the creature deserves this right. His speaking ability has won our hearts to his side.
This is one of the many impossibe but interesting parts of the novel. In creating a being without any past, without the influence of "nurturing," Shelley allows us to look at a pure moral nature interacting with the "world" then watch the "results." The creature supposedly learned language from his observations of the DeLacy family, a simple family enjoying the somewhat idealized Romantic life; he learns a "higher" form of English from his readings. These help him understand his own reality, make it clear to him that he was "born" physically deformed but morally intact.
Without the ability to speak in a language that is clear and sometimes elegant, the reader would not be able to understand the creature's plight as he saw it. In many ways, it is the means through which Shelley raises the level of sympathy for the creature; it also provides the creature with the means of understanding himself.
For comparison, Huxley does something similar in "Brave New World" where he has John the Savage learn English (and hence his means of understanding and expressing himself) though his reading of Shakespeare.
It is impossible to know the impact on "the reader" in general, but I can tell you that the monster's ability to speak eloquently put me on guard, seemed a sham from the start; see, I'm old to enough to have been snowed by smooth-talking poser-player monsters, and I'm educated enough to hear the echoes of Ugolino and Iago and to recognize the logical fallacies, the twisted Biblical parallels, the misunderstandings of Paradise Lost and of the Werther, the flat-out lies, false flattery, and feeling-based threats that shape his moral code of "Make me happy, and I'll be good"--sounds like a three year old's begging for a toy in a grocery store, whose next step, if denied, is to throw a tantrum. So for me, the monster’s eloquence prompted me to distrust him and to pay close attention to his words in my efforts to determine his nature. For fun, you might listen to Kristofferson's apt performance of his "Silver Tongued Devil": http://www.youtube.com/watch?v=bvCaQ0NQvzg