The US Constitution prohibits titles of nobility being granted by the US. At the time it was written did titles of nobility endow the nobles with:
Personnel: serf-type workers who paid rent on the land where they worked held by a noble?
Political rights: a seat in House of Lords, Commons or other similar legislative position?
Private property: land, house, estate?
Special use of public property: property owned by the King or other authority but used by a noble for residential or other special or private benefits?
I have a previous answer I've written to try to explain this thorny issue:
At heart, the origins of most titles relate to the rank/scale of the land that a given nobleman had administrative duties over. "Marquis/marquess", a title from the Continent, at one point referred specifically to noblemen who controlled land on the marches (borders); the title of "earl" in England comes from the early medieval ealdormen who were in charge of entire shires; "viscount" was likewise originally a continental title, and it once went to men appointed to assist counts with their administrative duties; "baron" has a complicated history in England, where it was imported by the Normans to refer to all noblemen who were (for want of a less loaded term) direct vassals of the king. By the High Middle Ages, though, English titles were becoming detached from these definitions of duties and simply related to a system of rank that gave each a specific position in relation to the others: dukedoms were invented to give to male relatives of the king a status, while baronetcies were invented for the other end of the system, and everything in between lost its administrative function. With the addition of more and more titles to honor men who'd done services for the crown or who'd paid for them through the late Middle Ages and the Early Modern period, even the association with related lands was often lost. (This did not happen to the same degree on the Continent - dukes ruled duchies, counts ruled counties, etc.)
It's hard to put into words what these titles were beyond "just things people refer to them as", because that's basically what they were by the point you're asking about - centuries later, Lord Melbourne would explain to the young Queen Victoria that one made a man a marquess if he merited high reward but shouldn't be made a duke for some reason. Titles often went along with incomes from rents from certain estates or with high positions in government, but all that they were intrinsically was a statement of social status relative to other titles or people with no titles at all. Henry VIII made Charles Brandon the Duke of Suffolk to raise him above the other noblemen at court, and to make it clear that they were very close.
I'm not sure what there would be to read, because nobody really explains it: it's just something you're supposed to understand from context. I think The English Nobility in the Late Middle Ages by Chris Given-Wilson might be helpful for unraveling this in more detail, though.
You are correct that titled people (above the rank of baronet, anyway) would have a seat in the House of Lords. The House of Commons was, as the name suggests, for people without titles, which in theory created a balance of power - but in practice, many (if not perhaps most) MPs were the untitled younger sons or sons-in-law of aristocrats, whose interests largely aligned with the lords'.
Apart from this, though, nobility did not confer inherent concrete benefits like the ones you're asking about. Frequently, individual noble families had a significant amount of property and money that was tied to the male line through strict settlements made every generation between fathers and sons, which made sure that nearly everything would be passed to the eldest son or, if there were no sons, the eldest nephew/male cousin/etc. This meant that when the Marquess of Hartingdon inherited the title of Duke of Devonshire from his family, he was also inheriting land, money, country estates and townhouses, and, in a sense, the tenants who had been renting from the estate - not because they were "serf-type workers", but because you don't evict your tenants for no reason. This was also about family lines, not titles in and of themselves: wealthy Americans of the period did much the same thing.