Could somebody explain this?

It is a crosstable.  The X'es means you don't play against yourself.  So player 1 does not play with player 1.  Each player plays with every other player two games.

It's a "Double Round Robin" - just like the recently completed Bilbao Final, only with 5 players instead of just 4.

A "round robin" event just means every player plays every other player.  A "double" means you play two games against each other player, one as White and one as Black.

It also says one player "advances," which would typically mean there is one or more other sections being played, and the winners advance to the next round.  But I don't see anything to indicate that - usually you can see the other sections and players, so maybe it's just a default reading for one winner.