Fragmented, Minimalist
Does the name James Joyce ring a bell? He wrote a truly epic novel called Ulysses. We only mention this because Joyce was a bit of hero to Beckett. In fact, Beckett was Joyce's assistant when he first started out. Needless to say, he was inspired by Joyce's use of stream-of-consciousness, a writing style that imitates our fragmented way of thinking.
It goes a bit like this: "Pizza—cheese melts like cobwebs—is that a spider?—Spiders are good because they eat flies—flies are gross—flies are really hard to kill—maybe I shouldn't kill a fly—who do I think I am killing another sentient creature—who am I?"
You can see the similarities between Winnie's manner of speaking and stream-of-consciousness. Winnie simply says what's on her mind and doesn't take the time to arrange it in a coherent manner, which partially explains why this play so doggone hard to read.
Fiona Shaw—you might know her better as Aunt Petunia in the Harry Potter films—once famously played Winnie and said of Happy Days, "One cannot know bits of Happy Days; it only works as a whole. It is not linear, and yet there are beautifully threaded modulations of feeling."
Beckett also liked to keep things simple, both in his writing and his set. He tries to use the least amount of words in the least amount of time (hence why his plays got shorter and shorter as the years went by). Beckett took great care and revised his work over and over and over again, which means that in this play, every word matters.