Empathy is an ability to sense emotion. An Empath senses emotion from physical contact (though some elves i.e. Keefe Sencen and Lord Cassius-don't have to make physical contact to sense emotion). Empaths can detect lies easily because of the guilt felt when telling a lie.
In Lodestar it is mentioned that humans' emotions are much more 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.
*Nightfall spoilers ahead*
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, however that everything is intense for an Empath and if they are not careful they can end up going numb.
Numb is feeling what others feel but not any emotion from them. This can mess people up, because emotions overlap and when the connection between Emotions, thoughts and memories, gets very hard to tell.
So, if they hugged someone or punched someone in the face, they'd feel the same.
Having an Empaths 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 surge of shivers. Though the difference is more noticeable when you figure out why your feeling it.
*this can be seen as a reason for why Vespera was able to do the things she did*