Active listening is a learnable and useful skill.
Most of the time we are predicting what people will say, and using the spare time to work out what we are going to say in return. This means that we often miss nuance or vital details.
This means that we can squander time or emotional capital by projecting our mental model of the person onto them. (this is a long winded way to say biases, but that triggers people, so I tend to avoid using that.)
So how do you active listen?
number 1) Slow everything down.
You do not need to reply instantly. Use non verbal queues to indicate that you are thinking and paying attention (nodding, saying hmm, etc, etc)
number 2) pay attention to non verbal cues.
Are they getting more fidgety? are they relaxed? are they looking more sad, can they keep eye contact? All of these cues give insight to the person's feelings. You should be able to spot if you are making sense, as they will change their pose/behaviour.
number 3) repeat what you think they are saying back to them to get agreement
"If I understand correctly you feel that [..] is that correct?"
You will need to pay attention to your body language and tone. Are you butting in? are you feeling angry? pity? annoyance? why are you feeling those emotions? is it better to come back later?
There are many more parts to active listening, but most of it can be learnt. Basically its practical empathy (as in understanding what people think, and why they might think that, rather than aiming to feel the same emotion as someone else.)