The stated goal was to levitate the Pentagon, meaning to lift it in the air, and Hoffman claims that they actually did and many saw the Pentagon rise... but you're not supposed to take that seriously.
Hoffman was a prankster, and a self-admitted fadist. He went from straight laced voter registration in the racist South, to being a leader of the New Left and anti-war movement in the late 60's and early 70's.
He felt that the old and new left were both boring and their methods were outdated. He had a better understanding of the new media environment of television, and importantly that America was a post-literate society.
He adopted a lot of the ideas of the diggers from SF. He captured the attention of the media with his outlandish claims and antics, on purpose.
He was a pioneer in street theater. Some of his actions include:
Running a pig for president
Throwing money from the gallery in the NY stock exchange so that the traders on the floor could be photographed greedily picking it up, to illustrate the complicity and greed of wall street (through the investment in defense companies that profited from napalm) in what he saw as genocide in Vietnam
A free speech activist, he was arrested for writing the word Fuck on his forehead and for wearing an American flag motif shirt.
He was also tried for incitement of riot in the Chicago 7 trial. He turned the trial in a circus through things like coming into the trial dressed in judges robes and other antics.
He did all of this in an attempt to politicize youth and drug culture of the 60's and mobilize it against the war.
An anarchist, he published steal this book, a book chock full of practical advice for avoiding corporate employment and living free through cooperation and petty scams like methods of placing free phone calls. All of this was based on the idea that American middle class values were fundamentally morally bankrupt and hypocritical, due to it's support of what he saw as an active genocide in progress.
He was brilliant, charismatic and somewhere between brave and crazy. Women loved him, and he loved them. And he loved drugs.
A rare specimen, of the same stock as the founders of this country. A person motivated by extreme empathy and a sense of justice, and someone not afraid to die for his beliefs.
He was a man with the same kind of creativity and media insight of someone like David Ogilvy, he could have easily made a fortune on Madison Avenue.
Instead his got his head beat in and his nose broken registering black voters. All the money he made from sales of his book and his fleeting celebrity were donated to civil rights groups.
The FBI and COINTELPRO had him under near constant surveillance and eventually caught him in a drug deal.
He skipped bail and went underground, and eventually emerged in the 80's and started working on environmental campaigns and against the Reagan administrations support of the Contras in Nicaragua (which was expressly illegal due to the Boland Amendment).
He was found dead due to an overdose of sleeping pills, but many think he was murdered.