Crossover district is one in which minorities constitute a sizable minority so that they can form a coalition with liberal whites to elect a candidate

Walter Jones writes in The Georgia Times-Union:

A crossover district, the Democrats said, is one in which black, Asian and Hispanic voters constitute a sizable minority so that they can form a coalition with liberal whites to elect a candidate of their choice. Republicans continually replied that the courts have only required maintaining the number of districts in which an ethnic or racial minority outnumbered the whites, so-called majority-minority districts.

And from the very recent post in the AJC:

Judges have been largely silent on whether the Voting Rights Act protects African-American “influence” districts, but former state lawmaker and labor commissioner Michael Thurmond — a veteran of redistricting — says Democrats should pursue the issue.
“It dilutes minority voting strength. It would be a novel argument, but it would be impactful,” Thurmond said.