Is there a branch of history focused on how people lived their day-to-day lives?

There is a field within historical studies that incorporates this idea. It is known as Social History. Social historians focus on the lives of "ordinary" people rather than the elite. Typical historical research focuses on the major players of history: Julius Cesaer, Constantine, Henry III, George Washington, etc. Social historians try and piece together the lives of the 99.5% of people whose stories often go unreported.

Unfortunately, I am not a historian or expert of the middle ages, so I cannot make any recommendations for resources into studying social history during this period. However, if you are ever interested in American Revolutionary era social history, just let me know!