It essentially is an informal term. The meaning in this context is that when the person who is talking about himself or another, says he is "not cut out" for a particular activity, they mean: "unsuitable" or "unskilled" at the activity. Hope that explanation was clear to you. Cheers.

It means you're not fit for it/suitable/capable for domesticity. Ex: I wanted to be a engineer but they said I'm not cut out for it because of my grades. ( not good enough, not fit for it, not capable )

"I'm not meant for" "Cut out" is more informal and colloquial.

It comes from sewing. Imagine that you got a piece of material and cut fabric pieces for sleeves and a collar and cuffs and a shirt front and back. And then you tried to make a pair of pants from those pieces. It wouldn't work very well because those pieces weren't cut out to be pants. The speaker is saying that they were not cut out for domesticity (being around the house, doing things like cooking and cleaning, raising kids, entertaining at home, etc.) When they try to do domestic things, they fail at it or they just hate every second of it. You can use the phrase "cut out for" to describe something you like and are good at and really enjoy ("I am perfectly cut out for this job!") or the opposite ("I am simply not cut out for hockey.")

"Domesticity is not for me" another way to say it :-)