Empathy is understanding things from another person's perspective. It's the act of getting inside another person's head and looking at the world through their perspective, rather than (or in addition to) your own. It's perhaps the most important facet of designing things, and therefore it's possibly the most important element of teaching, as teaching is what happens when our course designs actually come into contact with other people.
Or rather, teaching is what is supposed to happen in those cases. In reality, empathy is often the weakest link in the college classroom today and has been for quite some time, because the vast majority of actual teaching practice in our classrooms has a relationship with empathy that is best described as "avoidance".
What tends to happen in college teaching is this: First, we professors design a lesson by thinking about the content we need to cover. We make a list or a road map of some sort about it. Then we build a presentation that threads all the bullet points on our list, one that visits all the important towns and byways on our road map. Then we come to class and give our presentation; we get behind the wheel and drive to all the places we marked on the map. Later, we ask students to tell us what they know about the material, how much they remember or what they thought about the tour. Then repeat.
You may view this approach to teaching either positively or negatively, or a bit of each. There is room for debate about whether lecture --- which is the teaching method I am describing here --- is effective or not, how it could be more effective, and even what the definition of "effective" is. But there isn't much room for debate that while a lecture can be designed and delivered with empathy, empathy is not the default. Material and its coverage is the primary concern of the typical college lecture. The lecture, so conceived, does not really focus on the students until it's over. We ask them how they liked the trip and what they learned, having had full control of the wheel the entire time.
The best lectures are not the clearest ones, or the ones with the greatest command of the facts. They are the ones that connect with the audience on the deepest level, because the because the lecturer started with the audience in mind and kept the audience in mind throughout. The best college lectures ask questions like: What do my students need in this lesson? How can I connect this laundry list of material to their interests, even the ones they don't know they have yet? And how will I know, before the exam, that I have successfully connected with them?
Those questions show some empathy. "How will I get through all this material in an hour?", does not. At least, it's not the default.
You can absolutely build and deliver a lecture with empathy, but it's not the default --- not in actual university practice at least. But it's also not the form it remains in, if the lecturer does start with empathy. Once a lecturer starts designing her lectures with empathy, the lectures tend to begin to cease being pure lectures. If you start asking questions like How will I know if my students are learning what they need to learn? then the logical end of such questions is to stop lecturing so much, because a purely one-way transmission approach to teaching doesn't admit the possibility of answering that question. It leaves both you and the students deeply unsatisfied.
Instead, if we lead with empathy, the lecture naturally begins to morph into active learning. It may start with a basic think-pair-share activity or two. Then maybe you try out peer instruction. Then it becomes something further up this continuum like inquiry-based learning, case studies, programming activities, or something else. All of these active techniques are predicated on the idea of empathy, of involving the students in the task they are performing. That word "involve" means "to fold into", as a cook might fold a liquid ingredient into a soup or a souffle; "involving" a student in a task means entangling that student in the task so that the student and the task are inextricably linked. This is the ground on which empathy stands.
Over time, the more you explore the idea of leading with empathy in teaching, you may find that lecture shrinks in importance to fit a niche: a specific tool to perform a specific, small job in a moment of specific need. But not the default, and not the all-in-all.