blur - How to create blurring layer in adobe illustrator

I'm interested in Gaussian blur layer that blurring all inside of some figure located on this layer.

I mean, blurred background of some exact area. And in case of I move this area, blurred image must be updated. If I move some object in background - blur must be updated. etc.

Answer

It sounds like you want to use an opacity mask (accessed through the Transparency panel).

1. The masking object needs to be on a layer above the art it is masking. So, if you want to apply a Gaussian blur to the interior of some object, you would first make a copy of the object and paste in front (cmd-C, cmd-F).


2. Convert the "copied" object to white fill and no stroke.


3. Apply a Gaussian Blur to the "copied" object.



4. Select both objects (the copied object and the original object).


5. Using the Transparency panel, click the "Make Mask" button.

This will apply the Gaussian blur to the interior of the object. If you move the masked art, the masking object will move along with it.

Here's an Adobe video that explains and demonstrates how to use opacity masks. https://helpx.adobe.com/illustrator/how-to/illustrator-opacity-masks-transparency.html