Empathy is a feeling that most people recognise and believe they understand
The reality though, is that what many believe to be empathy is actually sympathy. Some people even consider empathy to be a feeling that can be switched 'on' or 'off' when they choose and 'used' when they so desire.
The concept of what we call empathy may well have been first framed by the German word 'Einfühlung', which in the 19th century, translated to 'knowing.' Today, the Oxford English dictionary translation has replaced 'knowing' with 'empathy.'
In 1903, the Philosopher Theodor Lipps called it "feeling one's way into the experience of another", and the Philosopher, Martin Buber, described an empathic relationship as an "I-thou" relationship (1984). He distinguished this from the I-It relationship, where the other person remains secondary to our own wants, needs or plans.
Buber's distinction helps us to understand the difference between empathy and sympathy: where empathy is feeling with someone in their trauma or suffering (I-thou) and sympathy is feeling pity or sorrow for them (I-It). You can find the link to a short video by the brilliant Brené Brown on this page that highlights the differences between sympathy and empathy.
Video: Brown, B., Sympathy vs Empathy - Brené Brown