[nf05papsjfVbc]

If you are able to put yourself in the shoes of the people to whom you are explaining something, the rest will follow. Consider what they already know and how you can bring them to your point by starting with something familiar and known.

If you have that point covered, the rest is "thinking clearly" and "expressing oneself clearly". These require practice as much as placing yourself in the shoes of the audience.

[cx42net]

I have the faculty to feel what others feels, and that's worse in my case. I feel when I lose them, which make me start to want to explain more, which in turn worsen the situation.

Maybe in that case I should try to stop that feeling and go with my initial idea ... while keeping in mind whom I'm adressing to (like you say in your comment)

[nf05papsjfVbc]

One aspect of placing yourself in their shoes is to feel how they feel. Another aspect is to see what they understand from what you are trying to explain. This requires a different kind of skill - of trying to see things from the perspective of different context, culture, skill, knowledge or language (do these words mean the same things for them?). It is this aspect that I had in mind and from your answer I get the impression that you meant the former instead.