What is this service and how I can be sure that my coins are safe with them? I thought that any online wallet or deposit is generally considered not viable method of keeping your coins.
As service, site or deposit can be hacked, and probably will at some point.
I don't think Circle offer a dedicated storage service like the Xapo vault and Coinbase's similar service. I know that both of them are insured for hacks at their end, I assume Circle is the same. There's still no way I'd keep decent amounts anywhere like that. I think Circle introduced limits on how much you could withdraw recently. They're moving more towards a USD layer on top of Bitcoin.