An honorific or sarcastic way to refer to society/the public; depending on context it can mean 'the world' or 'public opinion' (often used ironically).
そんなことをすれば世間様の目に触れるよ。
If you do something like that, the public will notice (lit. 'the eyes of society').
世間様はそう簡単に許してくれない。
Society/public opinion won't forgive that so easily.
彼は世間様に顔向けできないほど恥ずかしいことをした。
He did something so shameful he can't face the public.