When I've done it in the past, it was a vaguely tech-savvy law firm (the hard part isn't really the storage, it's the "evaluate the conditions of the escrow contract release terms".) (IIRC recommended by the customer but we had some independent validation - I think one of our VC's law firms had dealt with them before?)

We also had to details on how to actually build the product from the source, though I think they mostly just trusted us on that as long as we supplied a separate document - and by trusted, there were penalties spelled out in the contract about that too. (We were in good shape releng-wise but I expect a lot of companies would have to clean up their act to actually comply with that part.)

Escrow in general refers to a third party acting as an intermediary trusted by both parties. This works for source code, but also for money, goods, or anything else. Say if I want to buy a large diamond from you, you hand it over to the trusted escrow service, I give them a big pile of money. Once they have the money, they give me the diamond, and then give you the money.

Only in the case of source code, I give them the code, and they won't give it to you until I go out of business. They get paid for that, of course. In our case, we uploaded source code an escrow service's servers.