What did lieutenant cross mean when he thought that martha belonged in a world that was not quite real?

He means that Martha's world of her youthfulness and poetry can not be compared to the world to which the narrator belongs which is the world of war so there is a distinct between these two worlds ; they are opposite to each other .

His world has had most things taken away from it during war (because most things get destroyed when there is war whether it is grass, building and other things that make up the place) hence he can't relate to her world because it looks unreal to him.

All he has experienced is chaos, demolitions and death of even his own soldier friends.

just add on too that

explanation:

each year on march 8, international women’s day is celebrated around the globe. it’s an important opportunity to shine a spotlight on women’s involvement, contributions, and accomplishments on a range of issues from domestic violence to the role of women in the c-suite. the theme this year is “be bold for change”― a dictum that those who know me personally will acknowledge has pretty much been my mantra throughout my career on wall street, in media and most recently, in philanthropy.the empowerment of girls as leaders, who can be emboldened today to become even stronger leaders tomorrow, is an increasingly recognized imperative in our world, and it couldn’t be closer to my heart