I like this video as an explainer for what empathy is about (it’s 3 minutes). It’s not specific to design, but it is helpful for a quick understanding of what empathy is.
“Empathy is a choice… in order to connect with you I have to connect with something in myself that describes that feeling”
“Rarely can a response make something better… what makes something better is connection”.
It’s a sentiment that applies to design as well.
This is then a two minute video linking it in to the design process. It’s a great video for this topic: