Empathy is the special ability that allows an elf to sense emotion. An Empath senses emotion through physical contact, though some powerful elves like Keefe Sencen and Lord Cassius don't have to make physical contact with certain people to sense emotion (though this may only be with Sophie, due to her tweaked genes). Empaths can detect lies because of the guilt felt that comes with the lie; however, sometimes elves can evade this.
In Lodestar it is mentioned that humans' emotions are much easier to feel/detect and that an Empath can feel human emotions without touch. Sort of like how a Telepath can detect human thoughts without blocking.
On page 667-668 of Nightfall, Keefe tells Sophie something that his Empathy Mentor has warned him about, that with stronger Empaths there's a risk that comes with feeling too much and not having proper training. That the minds natural reaction for when things get too intense is to shut down. Everything is more intense for an Empath, and if they are not careful they can end up going numb.
Going numb is when you feel what others feel but you don't feel any emotions yourself. Say there was an Empath who felt that someone was sad. You might feel sad for them; someone numb would simply shrug it off like it had no meaning. This can mess people up because emotions overlap and with the connection between emotions, thoughts, and memories, it gets very hard to tell. If they hugged someone or punched someone in the face, they'd feel the same.
Having an Empath's ability (described by Keefe) can be like the rush of anger someone can feel is not very different from the rush of excitement; with the heart racing, and a surge of shivers. The difference is more noticeable when you figure out why you're feeling it. (This can be seen as a reason for why Vespera was able to do the things she did)