In The Age of Adaline (2015), Adaline watches some classic tapes.
Why is she watching it and who recorded it?
It's old newsreel footage...as marked on the film (not tape) cans.
The first purports to be 1906 newsreel made by the Edison company (as also marked).
A newsreel is a form of short documentary film prevalent in the first half of the twentieth century, regularly released in a public presentation place and containing filmed news stories and items of topical interest. It was a source of news, current affairs, and entertainment for millions of moviegoers until television supplanted its role in the 1950s. Newsreels are now considered significant historical documents, since they are often the only audiovisual record of historical and cultural events of those time
As for why she's watching it..well, firstly, it seems to be part of her job but mostly...
It's the story of her life, there's nostalgia there. It also serves as a convenient hook on which the movie tells us the story of her life.