I don't have a medical explanation for you, but I can tell you what it feels like. I've experienced many pangs of deep loneliness at times when I feel like I'm by myself and should be out being social. It feels like a tug on your chest. Like there's a void and some gravity is sucking things down into it. Or, I know it sounds corny, but something heavy sitting on your heart while you simultaneously experience anxiety.

When I am deeply lonely like this, in the moment, not just as a general idea, I definitely do feel it as a physical thing. I don't know if it's the same as what they're talking about here, but it seems reasonable that loneliness could be a type of depression, and I strongly believe that regularly experiencing the type of physical feeling described above could do damage to you.