Emotions are the source of empathy and connection. We cannot read each others thoughts, but we can feel each others feelings. This can work in different ways.
1. Feeling and form
We show what we feel in our posture, our gestures and facial expressions, even our voice. This also works the other way round: smile and you will feel slightly more relaxed, let your spine droop and your morale will drop a little too. When we look at someone we unthinkingly mirror their general demeanor. Sometimes we can’t help smiling when someone smiles, or yawning when we hear someone yawn.
So we have a chain here. You feel, you express, I copy your expression (a tiny little bit), and I feel what you are feeling (at least a little bit).
Incidentally, this is what makes portraiture so difficult. Painting a face is not intrinsically more difficult than painting a tree, but we look at the result far more critically because so much brainpower is dedicated to “reading” each other’s faces.
2. Imagination, or “as if”
If you tell me, your neighbour has just won a major award, I can imagine he must be feeling happy and proud. If you tell me he’s just been fired from his job, you don’t need to tell me he’s upset.
We can put ourselves in another person’s situation, and imagine what we would be feeling if we were in their shoes. It’s not accurate, as in many situations our feelings can differ, but it gives us a starting point.
3. Knowledge
We can learn to interpret signals. I remember a teacher whose jerseys came in two colours: red and …mud-coloured. When he was happy, he wore red. When the mud-colour came out, we knew he was in a foul mood.
And we can interpret language, such as journals or blog-posts, to understand what the person writing them is feeling.
* * *
When we look into someone’s eyes, when we imagine their situation, we can feel what they are feeling. Not only every man’s death diminishes me, but every person’s – every creature’s – pain is in a way mine and their joy also. This is where our sense of connection, and of oneness comes from.
To my mind this is what makes us human. Not that it separates us from the rest of the animal kingdom – e.g. dogs and dolphins share this trait – and why would we want it to? Being fully human is also being part of the big animal family.
I do not think we are rational creatures, but regardless of that I’ve always rejected the tag of “thinking thing”. As sentient beings, I think we are far more than that.
Stray Thoughts 
Have you heard of the nineteenth century philosopher William James? He believed “it is not that we see a bear, fear it, and run. We see a bear and run, consequently we fear the bear.”
Yes, I feel rather drawn to the pragmatists, though not to their way of seeing “truth”.
As for the bear: feelings arise by separate mechanisms. One is direct and another first runs things through the frontal cortex for interpretation, to find out what a situation means before flagging it emotionally. Running from a bear is likely caused by the direct mechanism that predates the frontal cortex in evolutionary terms. Emotions arising in social contexts are usually connected to the second one.