Back in the 1940s, Frank Sinatra drove young women wild, with his singing. They were known as "bobbi-soxers" and their hysterical reaction to Frank Sinatra's live performances in the early 1940a were similar to the estatic reaction the Beetles got when they arrived in the US in 1964. During the late 1940s, all through the 1950s and well into the 1960s, Frank Sinatra was one of the most popular singers in the United States. He was also a movie star and won the best supporting actor award for his role in the movie "From Here to Eternity".
Back in the 1980s, Joe Piscapo did a spot on impersonation of Frank Sinatra on Saturday Night Live skits. They were so popular, Joe Piscapo turned it into a stand alone stage show called "An Evening with the Chairman of the Board." Even more recently, Seth McFarland, the producer of the TV show Family Guy has shown his great love for Frank Sinatra and often incorporates his songs into that show.
There was also a recent (April 2015) HBO documentary called "Sinatra: All or Nothing at All". It is four hours long and provides as much detail as any of the full length biographies about the man.

Hi, sorry if this is against the rules, but if you want a musical point of view /r/Jazz is a good place to ask about him.