what does it mean when someone say for example: “This picture was taken by our very own (Name)”
I did not get it right!!
Thank you in advance 
“our very own <person’s name>” means that the person mentioned is, in some relevant sense, part of the same group as the writer/speaker (works for the same company, belongs to the same club, etc.) “our very own…” is an informal way of highlighting this connection.
So I can use it if a cousin of mine took a picture for example and I want to point out that it was taken by him by writing “this picture was taken by our very own (Name)”??
Give me some examples please where else I can use this idiom 
and can I put name of a friend or acquaintance instead of relative?
Thank you in advance
Examples would be as I mentioned: the person works for the same company or belongs to the same organisation. In those cases the person would generally not be a relative. I think it is possible to use the expression with relatives, but I wouldn’t wholeheartedly recommend it.