This article contains plot details from the latest book.
Empathy is the special ability that allows an elf to sense emotion. An Empath senses emotion through physical contact. However, if a person's emotions are particularly strong or if an Empath is particularly powerful, physical contact is not required. For example, most Empaths can feel at least some of Sophie's emotions without physical contact, as Sophie has stronger emotions due to her tweaked genes and human upbringing. Another example of this is in Lodestar, when Councillor Oralie is able to sense both Sophie's and Mr. Forkle's anxiety without physical contact when they are returning from visiting Gethen. She also senses Gethen's desperation for information about the Peace Summit.
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 that for stronger Empaths, there is a risk that the mind's natural reaction for when extreme levels of emotion are experienced is to shut down. Every emotion is for an Empath, and if they are not careful they can end up going "numb". When an Empath goes numb, they feel others' emotions but not their own -- for example, they may feel another person's sadness or anger from across the room, but their own emotions would stay the same whether they hugged someone or punched them in the face. Keefe speculates that this is what happened to Vespera.
When an Empath lies, their heart skips three beats -- one for guilt, one for fear, and one like a held breath, waiting to see if somebody will catch them. This physical reaction happens to all Empaths and is instinctive and unavoidable.
Having an Empath's ability (described by Keefe) can make a person's rush of anger feel equatable to extreme excitement or euphoria -- both release adrenaline and usually result in elevated heart rate or bursts of shivers. The difference is only noticeable when the Empath realizes why they are feeling these emotions.