Part of the issue in finding texts on this is that by the Victorian era, the nobility didn't really have "importance, jobs, and responsibilities". Apart from their right to sit in the House of Lords, they were not substantially different from other rich people, except that they tended to be even richer. The days when an aristocratic title indicated some level of administrative or military responsibility were long gone by the nineteenth century, and most scholarly work on that period focuses on the middle or working class. But, some things I can recommend for better understanding aristocratic life in the period:

Women and Marriage in Nineteenth-Century England, by Joan Perkin (Routledge, 2002) - not specifically about the aristocracy, but much of the book deals with marriages and women's lives in the upper classes

Dancing Out of Line: Ballrooms, Ballets, and Mobility in Victorian Fiction and Culture, by Molly Engelhardt (Ohio University Press, 2009) - that's kind of specific, I know, but social dancing was very important to the leisured classes

Aristocratic Women and Political Society in Victorian Britain, by K. D. Reynolds (Oxford Historical Monographs, 1998) - deals specifically with the way upper class women were able to involve themselves in politics

Aristocratic Century: the Peerage of Eighteenth-Century England, by John Cannon (Cambridge University Press, 1984) or Law, Land & Family: Aristocratic Inheritance in England, 1300 to 1800, by Eileen Spring (UNC Press, 1993) - you're probably going to get more information about specifically aristocratic society if you look for works about the eighteenth century, and some of it does cross over (for instance, the latter has an excellent explanation of the strict settlement, the means by which fathers ensured that their sons passed on property to their own sons, which definitely was still an issue to Victorians)