The way I always explain it to newcomers now is to start from digital signatures.
Digital signatures are useful, we all know that, now imagine if you could sign not only data, but also computation result. As in “I ran this code with these inputs and it produced that output”.
If you imagine that this would work, and it takes less time to verify that signature than running the program myself, you have a succinct proof.
If in addition you can hide some of the inputs you used, then you have a zero knowledge proof.
So ZKPs are “stronger” signatures as they can sign more than data. Sometimes a signature is enough, sometimes you need more. Sometimes you need privacy so you verify a signature inside a ZKP :D
Digital signatures are useful, we all know that, now imagine if you could sign not only data, but also computation result. As in “I ran this code with these inputs and it produced that output”.
If you imagine that this would work, and it takes less time to verify that signature than running the program myself, you have a succinct proof.
If in addition you can hide some of the inputs you used, then you have a zero knowledge proof.
So ZKPs are “stronger” signatures as they can sign more than data. Sometimes a signature is enough, sometimes you need more. Sometimes you need privacy so you verify a signature inside a ZKP :D