tr.v. dis·heart·ened, dis·heart·en·ing, dis·heart·ens

To shake or destroy the courage or resolution of; dispirit. See Synonyms at discourage.

Adj. 1. disheartened – made less hopeful or enthusiastic; “desperate demoralized people looking for work”; “felt discouraged by the magnitude of the problem”; “the disheartened instructor tried vainly to arouse their interest”

So basically it means discouraged.

Natalie has become very discouraged.

Lets say Natalie was trying very hard in algebra. She studied and tried her best but still failed the tests. Natalie would then become discouraged. She would feel as though she would never get it.