File > Append or Link?

I managed to bring material from other blend file. Does this mean do I have the copy of material? Or is it just a link where if I move the source file link gets broken?

It depends whether you append or link.
If you append, you have the material in the new .blend file and it is saved there and can be edited separately.
If you link, then the material is linked to, and if you edit it in the original file the changes are updated in the new .blend. I don’t know what will happen if you move the original file, but I guess it would be a problem.

The default is append, though for images(CTRL+F1) it is link. In the file browser window, there is a row of buttons at the bottom where you can choose to Append or Link.

To bring the external data into the .blend file, go to File>External Data>Pack into .blend file.

Thanks I will test them out.