As Catija mentioned in the comments, in the late 1920s/early 1930s, feature-length films were likely becoming increasingly prevalent due to improvements in movie-making technology. Indeed - again, as referred to in the comments - the first feature-length talkies began to come out, starting with The Jazz Singer in 1927. (For a more detailed review of film firsts, you can take a look at my answer to an older question here - you'll notice that the 1920s get mentioned a lot.)
As for the spike you see in the 1980s and '90s, there may be some bias due to the criteria for inclusion on the graph (namely that at least one imdb user had to have rated it, and many users may be more familiar with '80s and '90s films than with earlier ones).
But if there's an explanation beyond that, it may be due to a couple of factors. First, as Wikipedia says, "The decade of the 1980s in film saw the return of studio-driven pictures, coming from the filmmaker-driven New Hollywood era of the 1970s." Second - again working off of Wikipedia information (sorry, I know it's a less-than-ideal source...) - films in the '80s were building off of an increase in popularity of certain genres that began in the '70s. Several genres experienced "booms" that decade, often with the help of popular movies from the '70s - sci-fi series like Star Wars and Mad Max began in the 1970s, and their sequels continued into the 1980s, often to wild success. This perhaps inspired much of the boom in sci-fi and blockbuster films during the rest of that decade, which in turn may have contributed to the apparent overall boom in movie production. (Though you'll also notice in Wikipedia's list of trends that many other genres saw increased attention and production, as well.)
You may also notice that the '80s seemed to see a spike in movie sequels - perhaps due to the popularity of the sequels (such as the Star Wars movies) that came out early in the decade. The realization that sequels could be huge money-makers would certainly explain a lot of the movie trends in the following decades, as well as the general spike in movie production in the '80s and '90s.