There is a long in depth discussion here:
The Day the Music Died is the name McLean gave to February 3, 1959, the day an airplane carrying musicians Buddy Holly, Ritchie Valens and The Big Bopper crashed, killing all three. But, as he explained on his web site, the date has a profound meaning to McLean because it marked a major change in his life:
"In Don's life the transition from light (the innocence of childhood) to the darker realities of adulthood probably started with the death of Buddy Holly and culminated with the assassination of President Kennedy in 1963 and the start of a more difficult time for America."<3>
From the standpoint of about 1970, the twenty-five year old songwriter recalled the effect of six transitions on the day the music died, noted at the end of each verse of "American Pie".
* In the first verse, McLean tries to remember how he felt when Holly, Valens, and The Big Bopper died when he was a thirteen year old boy: But February made me shiver with every paper I delivered; and I can't remember if I cried when I read about his widowed bride (referring to Holly's pregnant wife Maria Elena Holly). But at the end, all he can say is, But something touched me deep inside the day the music died.
* At the end of the second verse that describes McLean's perceptions of middle class America during the mid- and late-1950s, McLean believes that events after the day the music died would portend to bad times ahead: But I knew I was out of luck the day the music died.
* At the end of the third verse that focuses on the rise of Bob Dylan, McLean speaks for a generation of songwriters and musicians that misses Holly, Valens, and Richardson: And we sang dirges in the dark the day the music died. Since McLean is from New York, it's also possible that he was referencing The Great East Coast Blackout<4> which began when the northeastern region of Canada and the United States was plunged into blackness at 5:16 p.m. on November 9th 1965. It was the largest single power failure in history that plunged thirty million people (one-sixth of the population of North America) in eight American states and the eastern portion of Ontario into total darkness.
* At the end of the fourth verse, where McLean witnesses the effects of drug use on rock music, he asks if there was some higher meaning related to February 3, 1959: Do you recall what was revealed the day the music died?
* After McLean witnesses a murder and beatings at the Altamont Free Concert in December 1969, in the fifth verse, he says that Satan was happy on the day the music died: I saw Satan laughing with delight the day the music died.
* Finally, at the conclusion of "American Pie", McLean sees Holly, Valens, and The Big Bopper off to heaven on February 3, 1959: And the three men I admire most:/ The Father, Son, and the Holy Ghost, / They caught the last train for the coast the day the music died.
The Trinity
The final verse of "American Pie" includes the lines:
And the three men I admire most: The Father, Son, and the Holy Ghost,
They caught the last train for the coast the day the music died.
The three persons are an allusion to the Christian Trinity. The interpretation that is most consistent with song's events is that the three persons are The Big Bopper, Ritchie Valens, and Buddy Holly, respectively. Specifically, The Father is The Big Bopper, who was the oldest of the three musicians, as well as being the only father. At the time of Richardson's death at age 28, he had been married to Adrian Joy Fryon for over six years, and the couple had a daughter, Deborah, and were expecting a son, Jay Perry. The Son is Valens, who died as a child at age seventeen. The Holy Ghost of rock and roll is Buddy Holly because of his pervasive influence on that music (and it may very well be a pun on his name, "The Holly Ghost"). Holly was an original inductee to the Rock and Roll Hall of Fame. Their travel on "the last train for the coast" is a metaphor for death (a train, in dream symbolism, is traditionally interpreted that way), with the coast representing heaven as their final destination.
Numerous other trios have been suggested, the most popular being the three American leaders assassinated during the 1960s: President John F. Kennedy as The Father; his younger brother Robert F. Kennedy as the Son; and the Reverend Dr. Martin Luther King, Jr. as the Holy Ghost.
http://en.wikipedia.org/wiki/American_Pie_(song)
I really don't know how RFK could be JFK's son!
However, McLean's line, "The courtroom was adjourned, no verdict was returned." in my mind refers to Lee Harvey Oswald assasination, which mooted any trial on the claim he killed JFK.