In the United States, there are many published books about the history of towns, counties and cities, which cater to the interest of inhabitants about their local history.
Similarly, many towns, cities, and counties have Historical Societies or Historical Commissions that rely on interested volunteers. These societies are often engaged in efforts to preserve historic properties, erect memorials for significant local events and persons, and historical outreach to the community.
What do these societies teach us? Does approaching the history of small communities give us a different perspective than we would get when viewing things from a national or continental scale? Do we appreciate history differently through the preservation of buildings and artifacts, rather than as a written narrative?
Another part of local history not mentioned above are genealogical societies. These enthusiast organizations often preserve demographic information, especially pre-1800, that can be very difficult or time-consuming to collect otherwise.
Having these small groups that preserve local history helps to give people a sense of how the community fits into the larger narrative of the national history. It also helps to provide a stronger sense of community, giving them an identity on the smaller end of this perspective. The preservation of these local buildings and locations also allows people to connect on a more personal level with the history as they can see and appreciate what it was that happened or the effort that it took to accomplish the thing that happened, as opposed to just having a short text entry about the subject which is very impersonal and doesn't get people involved in the history of the event or place. It is easier to related when you can see or feel the thing that is being described. I will admit I only have a Bachelors degree in history so I may not offer the fullest of insights on this, but this is what I feel is the importance of these groups and how they benefit the local communities that they serve.
I have done volunteer work for the Historical Museum in my town and it decently popular. These small local museums provide a much smaller perspective then what big museums can do. The main exhibit we have now is about the architecture of the city and all the examples of the different styles. You could look this stuff up online or in a book but it is very different when you can see all the familiar buildings and you can relate to the topic better. There a greater sense of relatability.
At their best, local historical societies can tell more intimate stories that a broader approach ignores - either tied into an overarching historical narrative (discussing local factories and mills in relation to the Industrial Revolution, for instance), or presented more simply as "stuff that went down in this place".
I do think the public becomes more engaged with the past through seeing artifacts, if they're properly contextualized. That's where "at their best" really comes into play - it needs more than just "this is from 18XX, made in this decorative arts style, donated by so-and-so". I mean, by all means try to teach about decarts movements, I love them! But you want to try to guide people into thinking about these objects in terms of what they meant to their original owners, and into imagining the experience of seeing/using them on a daily basis. While visiting an exhibition at a larger museum that looks at things on a national scale can spark an interest in the smaller picture, it still leaves the smaller picture vague, while an historical society exhibition should be able to fill in that small picture with detail and texture.
Sorry, this is kind of rambly. Right now I'm working on an exhibition about the inhabitants - rich and poor - of a particular street in the town where my museum's located, and I have a lot of feels about connecting to the past on a personal level.