How to understand this new phase format table in cricket world cup 2019?

It is similar to sessions in test cricket, but here 10 overs are considered to be one session or a phase. The team dominant throughout the session wins it, mentioned in the column below the team's name and notable contributors of that session are mention in the third column (Bumrah and Williamson in the above picture). It is used to analyse the progress of the game and for comparison of both the teams performances at different times during the game.

Yes,the phases are similar to sessions in Test cricket.in one day match 10 overs are considered as a session.hence five sessions in one match.The team which dominates respective phase is the winner of that phase.The player who performs best in respective phase is the best performer of that phase.Like Bumrah in 1-10 overs and Williamson in 10-20 overs.