No one knows for sure, but it's almost certainly political grandstanding as Ryathal discussed.
This article explores some of the possibilities.
First of all, it wasn't technically a filibuster of the Patriot Act, because that bill wasn't on the floor. The US Senate has rules which allow a senator to continue speaking as long as they want, about any subject they want, until they physically can't any more or 3/5 of the Senators vote to stop them (cloture). Additionally, a bill can't be voted on until debate on it is over, which means that as long as there is at least one Senator willing to filibuster, then the bill can't be voted on. There's other ways to avoid it, but that's the general scenario. So while it was a filibuster (nothing else could get voted on), it wasn't really a filibuster of the Patriot Act.
So, what did this filibuster gain him, since it didn't prevent the bill from coming to a vote?
If [Sen. Majority Leader Mitch] McConnell was going to push for a quick vote on his bill for a "clean" reauthorization of the Patriot Act, then Paul gummed up the works. But that probably wouldn't have happened anyway, since the House is departing for the holiday weekend at 3:00pm today.
Still, the large and unexpected delay caused by Paul and his supporters puts the Senate in a major time crunch, which some observers have argued will have political effects.
The delay may have put the Senate into a situation in which it can't consider any bill except for the House-passed USA Freedom Act, which limits bulk surveillance, between now and Saturday due to complex procedural rules explained [here].
One theory, based on the timing (it ended before midnight) and the fact there wasn't even an attempt to bust it by invoking cloture goes:
It’s quite possible that [Paul and McConnell] made an agreement to get themselves out of holes they had created for themselves... By appearing to be left with no choice but USAF, McConnell could then whip it, and ensure it passes, to be quickly sent to Obama for signature. If McConnell really whipped it, Paul could even cast a symbolic vote against it.
In other words, it's possible that it was a way to force the bill through while letting Paul still go on the record as opposing it. This is just a theory, but it would explain the oddity of it.
That then feeds back into the "political grandstanding". Regardless of whether there was any ulterior motive, by publicly filibustering about the bill, he shows his opposition to it, thereby encouraging his supporters.