I prefer the concept of keychain that Andreas Antonopoulos used to explain what a wallet is:
Stefan Tilkov: So even though I'm dragging this out a bit, I still want to ask about one or two technical terms... One that everybody mentions is the wallet. What role does the wallet actually play? Does it store my money, or what does it actually do? What is it, from a technical standpoint?
A. Antonopoulos: So it's a keychain; from a technical standpoint, it is a keychain, first and foremost. What most people call a wallet doesn't store coins. The currency is never in the wallet, it's always on the blockchain, it's on the global decentralized network. Everybody can see all of the coins that are sitting on the ledger, everybody has a copy of the ledger... Everybody has the coins, they just don't own them. What they own is the keys that allow them to make digital signatures to actually spend these coins. So your wallet is a keychain; first and foremost, it stores private keys. It calculates public keys, it calculates public addresses, and it's able to apply digital signatures on transactions to prove that you are the authorized owner of those funds. But in order to do that, it also has to be able to receive the state of the blockchain and understand which of the coins that your keys control have been spent and which ones have not, so it can construct this second-layer abstraction which is a balance. Bitcoin doesn't have a balance, there's no account; you have to count all of the coins that you can address with your keys, and say "Okay, it looks like I can move this much total", but it's maybe stored under a hundred different keys that can sign for these coins.
See:
https://www.case-podcast.org/16-bitcoin/transcriptOne can envision that, if someone gets hold of your keychain, or you hand out the (private) keys, they can duplicate your keys or steal whatever they give access to. As an analogy, that may work. The problem is though how to lay it out in layman’s terms to a complete neophyte. I mean, as one gets to know the ropes a bit, he can understand that there are TXs that need to be signed and so forth, but from a real beginners point of view, for somebody who is never going to get to know the technicalities well, neither a wallet not a keychain facilitate signing transactions in real life. Even hinting that Bitcoins are not really coins is too confusing for many to assimilate …