First, a warning: the concept of fakelore is outdated and is no longer used by academics.

Folklore represents culture (e.g. stories, songs, and jokes) that are spread "person to person". Often this means oral tradition (i.e. culture that is spread by word of mouth), but folklore can also include things like internet culture, where culture is spread person to person through technology like email.

One of the problems that scholars of folklore face is that people have a tendency to claim that stories that were the work of a few artists actually represent oral tradition. Sometimes people will take existing folklore that was spread by word of mouth, but then modify it: the brothers Grimm are famous examples of this. Other times people will create entirely new stories by themselves but then pass them off as new traditions: famous examples of this include the Kalevala and the Paul Bunyan stories.

The folklorist Richard Dorson was very frustrated by the counterfeiting of oral tradition, and created the term "fakelore" to refer to stories that claimed to be oral tradition but were actually the work of a few people.

The problem with this split between folklore and fakelore is that fakelore can find its way back into the oral tradition. For example, although the story of Paul Bunyan mostly originated as advertising for logging companies, it eventually entered oral tradition in America. Another interesting example is the "Eagle Dance", which was taught to the Washoe Indians by a movie director, but since entered their oral tradition. It doesn't make sense to dismiss "fakelore", because in reality it plays a huge role in the creation of oral tradition.

Because of this, the concept of fakelore is no longer used by folklorists. It's OK to point out that oral tradition doesn't always originate from oral tradition. But the word fakelore is often used to imply that some oral traditions, just because they were originally the work of a few people, are therefore not "real" folklore. In that sense the concept of fakelore is deeply flawed.

If you are interested in learning more, Alan Dundes has an article titled "Nationalistic Inferiority Complexes and the Fabrication of Fakelore" that is available online at JSTOR. JSTOR is behind a paywall, but can be accessed for free from some local libraries.