Well, in the world of Bitcoin, owning BTC basically means you have control over a private key that can sign transactions for a certain bitcoin address.
So even if someone isn't tech-savvy or doesn't fully understand how Bitcoin works, as long as they have access to their private key (or to a wallet that stores this key), they "own" those bitcoins.
To prove it? They could sign a message with their private key - sort of like an electronic signature. Anyone could then use the corresponding public address to check that this signature is valid.
But remember: Private keys are super important and need to be kept secret! Never share your private keys or your wallet password with anyone. That's rule number one in Bitcoin land!