It appears that buckets are groups of documents and other evidence compiled during Republican Controlled House Committee investigations prior to 2018 elections.

1 - Russia-related documents (the ones POTUS walked back on declassifying)

2 & 3 - Emails showing knowledge about withholding information from the FISA court. (Exculpatory evidence)

4 - Emails between FBI, DOJ and others that clearly show that they know about information that should have been presented to FISA court.

"Other Three Buckets"

-Documents Nunes and GOP allies have pushed Trump to declassify. (POUTS made a declaration on these but reversed course)

FISA Applications

FBI 302s

Gang of Eight Material

I suspect the 5th bucket to contain one or all of these. With perhaps up to 2 more buckets with unknown contents.

https://www.washingtonexaminer.com/news/sean-hannity-says-sources-tell-him-extraordinarily-damning-coming-out-about-doj-fbi

https://www.washingtonexaminer.com/news/devin-nunes-fourth-bucket-of-classified-emails-show-info-withheld-from-fisa-court