This part in my cars engine is open, and the stone like substance is cracked.

Is this an emergent issue, what is its purpose?

(noticed this while changing out my light bulbs)
Thanks

 

First off if that's your engine bay, wow, very beautiful. Anyways I think that's one of the engine mounts? Try searching on the parts.lexus.com website. In fact maybe I found it here?

 

Welcome! That's not a 5th gen ES350, that's very much a 6th gen engine bay. You can tell because there's no power steering fluid reservoir and the coolant overflow tank is at the front of the bay.

The part you circled is the upper engine mount, probably part number 1236331033, it's purpose is to stop the engine from moving around inside the engine bay. Cracks are sometimes OK as long as there isn't material falling out or the crack isn't all the way through, but get a trusted mechanic to take a look (which he should do for free because it's a quick peek) and advise on whether it needs to be changed or not.