What do people mean when they say "Everything is connected"?

I don't know if this is the best stack exchange for this type of question, but I couldn't think of a better one. If there is a better one, feel free to migrate this question there. Anyway, here is my question. A lot of religious and/or spiritual people say the phrase, "Everything is connected". But what does that vague phrase actually mean? It seems to be so nebulous as to mean lots of things, and is resistant to either verification or falsification. I want to know what people mean by that phrase. Again, if there is a better stack exchange for this question, let me know, or feel free to migrate it to there.

I always find this confusion confusing. Your typical physicist would have no problem asserting that (say) Jupiter's gravitational pull affects every speck of matter in our solar system, or that the entire universe is connected by forces that originated billions of years back in time. The entire notion of a 'field' in physics implies connection across any range and in every direction. And no one really disputes that a single change in an ecosystem affects the entire ecosystem, or that a change in one part of the human body affects the entire human body. People recognize that systems are holistic, and that holistic systems change as a whole, not variously by individual parts. And yet, if the same thought is presented in any non-hard-science context, people roll their eyes and shake their heads in dismay.

Part of the problem is that self-oriented egoism is baked into our self-perceptions. We think of ourselves as unique, independent, unfettered, reasoning beings — as though we were hatched from eggs as fully-formed adults — and thus that we have no necessary or intrinsic relationship to anything other than ourselves. But — and this is karma 101 — that's clearly not true. Everything we do has an impact on others, if only in small ways, and everything others do has some small impact on us. If I'm brusque with someone it upsets them, and being upset they are brusque with someone else, which upsets them; my act flows out like ripples in a pond, diminishing over time until it fades into background noise. And that's true of the roughly eight billion people now living on the planet, and of all of their ancestors. A man in China has a fight with his wife (because of a relationship style he learned from his parents, who learned it from their parents…), so he's distracted at work and makes a mistake; a year later the product he worked on fails, badly injuring someone in Sweden, and that Swedish woman turns sour and makes everyone around her miserable…

As a spiritual teacher once said, consciousness is a field, not an isolated point. It encounters every experience around it; filters, absorbs, and transmutes it; responds with activities that become experiences for others… We have an ability to work with that, to mediate how we filter, absorb, transmute, and respond to experience, but we cannot escape from the field any more than earth could ever escape Jupiter's gravity.

I think that to know what an individual means by connected, you really have to ask them how. It can mean anything from our all being in the same universe with interactions limited by forces, relativity, and quantum... or it can mean something completely supernatural.. or just about anything else.

If they can specify what the connection is, you can evaluate it on the merits of the claim. If they can't, I recommend ignoring them.