Conjunctions should be used to conjunct two different parts (sentences, words, ...) so, technically speaking, starting a sentence with them is broadly considered a misuse.
But exactly for being a misuse, such construct has the effect of drawing extra attention on the sentence itself.
Using the form
as opposed to
SENTENCE_A e SENTENCE_B
immediately highlights the absence of a sentence joined before it and makes the reader wonder what the author omitted.
Such omission can be for instance the situation in which SENTENCE_B takes place, and we find many examples in poetry.
As an example , G. Pascoli starts his poetry Il gelsomino notturno with
E s'aprono i fiori notturni,
nell'ora che penso ai miei cari
The sentence after the E describes something happening at night, but there a whole lot of content unexpressed before it, namely the situation of waiting during the night, before the flowers disclose.
In this other example 
E, dopo tanti discorsi, finalmente l'accordo!
The conjunction E implies a phase of discussion before the deal. Using the E allows the writer not to explicitly mention it, but rather to suggest that the current situation is a consequences of previous events.
 Examples taken from http://www.accademiadellacrusca.it/it/lingua-italiana/consulenza-linguistica/domande-risposte/sulluso-congiunzioni-allinizio-frase