Moving element when mouse on it

Does somebody can help me to achieve the same or similar effect as here :
Whit the element moving when mouse is on it?

As we normally ask on the forum, what have your tried yourself?

I tried to do smth with jquery mouse effects but all that looked like a kid playing with a sand.
But I want to read or heard from somebody how to do things like that? With more CSS or more JS. I have no idea how to achieve this so to be clear all I tried with jQuery has no sense. That’s why I ask here in hope of some help or at least some docs to read on this because I can’t find it by myself on web

or just at least will be happy if somebody can show me the direction where to find solution

If you want to recreate what this site has done, then I suggest first reviewing their source code and try to understand why it works the way it does. Copy the code into a Codepen and then manipulate the code to “see” how it works. Keep in mind that the source code when unminified, is about 46,500+ lines of code.

When you write what you did above, we do not know what the element you are trying to move in a similar manner as the example you showed us. That is why we ask you to show us what you have and explain exactly how you want the element to make when you mouseover or click the element. The more specific you are about what you want, the more responses you will get from a particular question.