The proles are the working people -- the ones who provide all the more physical and manual labor that needs to be done in the society. For example, they serve the food at the cafeteria at Winston's workplace. They make up about 85% of the society.
To me, the main importance of the proles to the story is that Winston thinks that they are the society's hope for the future. He seems to think that they are more closely connected to what people used to be like -- they have more "human" lives than they people in the Party who are constantly monitored. He thinks that they are much more likely also to be able to get together to start a rebellion because they are not monitored.
The proles are the great mass of people who are not members of the Party in Oceania, and yet who make up the bulk of the population. The Party more or less dismisses them as of no importance. Winston harbors the romantic illusion that the proles will revolt and take down the government. In "The Book," however, we learn they are kept too poor and ignorant to mount any kind of ideologically coherent campaign to overthrow the oligarchy in power.
The proles, however, are more important to the plot than simply as representatives of the downtrodden masses in this dystopic world. In the world of the proles, Winston finds remnants of his dimly remembered childhood before the Party gained control. He buys a diary and a paperweight with a piece of coral inside it from the proles (or so he believes). He and Julia rent the room above Mr. Charrington's shop and, for a brief time, recreate some semblance of a normal, old-fashioned love affair.
But the Party's secret police also use the proles as a cover to nab transgressors like Julia and Winston. We learn that Mr. Charrington is not a prole but a member of the secret police. While we are never told so definitively, Orwell strongly hints that the washerwoman endlessly hanging diapers in the courtyard below their window at Mr. Charrington's is also a spy: Winston has to creatively invent more and more grandchildren for her to justify the amount of laundry she hangs. Proles thus become both romanticized symbols of the past onto which Winston projects his fantasies, ideal "covers" for a spying secret police, showing how far the network of surveillance has spread, and a mass of suffering people living in miserable homes and enduring rocket attacks.