“That was passed down to me by my grandfather.”
You have an antique gun that used to belong to your grandfather. You have visitors from your church over at your house, and someone is looking at the gun. You explain where it came from.
That was passed down to me by my grandfather.
When people give meaningful items to their children, grandchildren, nieces, nephews, and so on, it's called "passing ___ down". People "pass down" things like:
For things that are valuable but don't have much emotional meaning, we don't use the phrase "pass down". Instead, you say that the relative "gave" or "left" someone these things:
My parents left me a little bit of money when they passed away.
To explain who gets the item, use "to". Use "by" to explain who is giving the item:
It was passed down to me by my mother.