A good example is face recognition on your phone,
or in face recognition systems in general.
The way they work is pass in infromation and tighten the channel width for information throughput, performing a compression of the input face features.
Then try to reconstruct the input on the other side by learning a decompression transformation.
If you're able to recreate the input features perfectly with less vectors representing that input, then you've learned a more ideal and abstract representation of the facial features.
The reason this is considered unsupervised is because the human is not trying to influence how it does this using their own reasoning. It's [face in --> compress --> decompress --> face out --> is face in the same as face out]. It's not "learning to find patterns". It's learning to create better representations.
A network that passes through, compresses and decompresses faces accurately is useless, but the intermediate compressed representation is VERY valuable. You'll hear about the compressed representation refered to as an embedding.
Facial recognition systems don't compare noisy input, but the pure representations that filter out noise and capture abstract representation. So well that the same face will end up with compressed representations that resemble that same face taken in slightly different angles, with different hair styles or colors. etc.
If a face
embedding vector is close spatially to another face
vector then it is similar in the abstract, not just circumstantial, sense.
You can now use spatial lookups on compressed face representations to do automated watchlist queries on camera feeds. If a camera face, when compressed, looks similar to a watchlist face, then send an alert.
Similarly you can compress the face on an ID, the see if it's similar enough to a face extracted from a selfie to do two factor facial/identity verification.