They mean "unsolved" in the sense that for eg we cant prove or disprove claims like "all integers are the sum of three cubes".
Every cube is within one of a multiple of nine, which means every sum of three cubes is within three of a multiple of nine. So numbers of the form 9k+4 or 9k+5 cannot be expressed as the sum of three cubes.
It’s conjectured that every other whole number can be.
https://twitter.com/robinhouston/status/1169938974246342658?...