This is a big question relating to four very different short stories, so my answer is going to be necessarily brief. I will point towards general patterns rather than specifics, and this will hopefully enable you to return to these four excellent stories and analyse them further.
Katherine Mansfield is an author who is rightfully famous for the way in which she is able to depict the limited position of women in a patriarchal sphere. Often she is able to do this incredibly poignantly, as in "Miss Brill," where the title character is really shown to have such an empty life, devoid of joy and human companionship. This is indicated when Miss Brill returns home to "her room like a cupboard" alone and saddened, after having had to imagine all sorts of things to make herself believe that she is significant and needed.
"The Little Governess" again is another story that reinforces this central idea. The way in which the governess is only refered to as the "little" governess emphasises her lack of strength and power, and as the story progresses we see that she is subject both to male power and also she is economically dependent on Frau Arnholdt for a job. She is abroad for the first time, and thus weak and vulnerable in every sense.
"The Garden Party" seems to emphasise the naivety of Laura at the beginning of the story through the way that she is blind to the impact of class. Her shock at the death of Mr. Scott and her desire to cancel the garden party results in her being reprimanded by her mother and scorned by her sister. It is only at the end of the story, when she goes to pay her respects and sees the corpse of Mr. Scott that she experiences an epiphany that comments directly about the value of her frivolous life.
Lastly, "Her First Ball" depicts the way in which growing up is a very ambivalent experience, tempered as it is by both excitement and joy and also an increasing awareness of the ephemeral nature of youth and beauty. Leila's response to the fat man's comments and her desire to leave the ball reflect the latter, whilst her return to the dancing and her forgetting of the old man indicate the former.