as a particularly sensitive empath (based on my neurology) let me clarify once and for all.
i agree with daniel birdick that it's an act of imagination, and some have a stronger imagination based on having more sensitive responses to stimuli. those with a lower pain threshold are likely to possess a stronger, shall we say, sympathetic/empathic imagination. the imagination then feeds an emotion, perhaps turning sympathy into empathy. however you will never know exactly what the other's pain is like in the moment they are feeling it. that would be absurd.
and in certain situations, you can literally physically shudder when you see someone stub their toe for example. again, imagination feeding an emotion.
some empaths literally take on the feelings of others, like it's infectious. if i really love someone, i will take on their pain or happiness often more so than they feel it themselves. is that sick? lol. especially if, for some reason, i can't comfort them when they are sad, it's like the energy has no one where to go so stays in me.
i agree that there are posers, neither here nor there, who espouse a lot, but actually feel little. motives are everywhere, and manifest themselves in all manner of hypoctrical, self-decieving or downright calculating ways.
since i know i have excessive sensitivity to other people, i quite happily admit when i do not care, or no longer have the energy to care about a situation I can not help. irony of ironies, I am setting myself up for the possibility that someone will deem me heartless. it is often the ones who talk about caring, as opposed to actually caring, who you should watch out for. for those unskilled in emotions, they can get confused, and (like many socios do) resort to calling everyone insincere.
i am not perfect, I don't really apply my imagination to certain people's pain, like my mum for example, and there is obviously some reason for that that I do not understand. it was this that made me think I had something wrong with me.
shutting off empathy is a defence mechanism, when things go beyond what you can physically handle.
but yes, empathy exists to a degree, for you can't replicate exactly the other person's inner life. otherwise, imagine seeing a dead body then dropping dead yourself - that's complete empathy, and well, that's useless.