It is a soft squishy term more akin to marketing than practical, in the vein of "Experience the Culture of..." and similar in squishyness to "Live Like a Local..." Basically it is an attempt to do something that can't really be done, and to say you experienced the culture of "X" will immediately begin a refrain of "Well you did not really experience the true culture"
For example, go to Munich and experience the culture of going to a Beer Garden or Oktoberfest, that is certainly a cultural event, a long history, something even some Germans do, but many would tell you that really does not represent current German culture, and only the historical culture of one region (maybe city) of Germany, others would tell you it is a drunken tourist spectacle that has nothing to do with current German Culture.
Certainly you can go someplace, eat the local food, drink the local drink, take a tour and learn the history, see an exhibition of the local dance in quaint costumes, and get a sense of what is presented as the local culture; but the real culture is much more mundane, but rich. The locals likely do not eat that food often, drink little of that local drink, they probably eat at McDonalds and drink cheap big brewery beer, listen to Pop music, and complain about politicians. Many of them likely do not look like what you think a "German" looks like, but German they are. Experience the culture? Sure, get a job, scrape to get by, put up with tourists, worry about what the politicians are going to do next, basically live life.
Same with "Living like a local", you can't, certainly not in a week, or a month, even if you live in a quaint village for years, you will still be on the outside looking in, and you likely will be doing it from a position of privilege, not worrying about paying the bills or having to work.
But to cut the gloom, there is no shame in going somewhere, eating good food, having good drink, having something different than what you can get at home. Good to learn the local history, support the tourist culture presented, the museums, get a sense of maybe what was. Did you experience the culture? Does it matter? Also be sensitive to the people who live there, they are not workers at a Disney attraction, they are just living life, likely have never been to the local museum (except on a class trip in primary school maybe) or have been to Oktoberfest, they may not even own a set of Lederhosen.