Essentially, the DNC decided to shake up the primary season by shuffling the traditional order of primaries, and had South Carolina as the first primary in February. New Hampshire has a state law requiring them to be the first primary, so they could either break state law or defy the DNC. (Keep in mind that parties are technically private organizations, so I don't know how state law can force them to do that, but American elections are weird, and I'm Canadian.) The Republican-controlled NH government decided on defying the DNC, so although they technically held a primary, it was not sanctioned or authorized, and thus the DNC disallows contenders from appearing on the ballot, which Biden complied with. I believe the DNC has also invalidated the electors as a result, so they might not even count them at the convention.
TDLR; DNC changes primary schedule, Republican NH says "by law we go first", DNC declares NH primary unsanctioned and tells candidates to stay off the ballot.
I was thinking Austin McConnell