CBOR is when you need option for very small code size. If you can always use compression, CBOR provides no significant data size improvement over JSON. With small code size it beats also BSON, EBML and others.
Or compute. Compression isn't free, especially on power constrained devices. At scale power and compute also have real cost implications. Most data centers have long been using binary encoding formats such as protobuf to save on compute and network bandwidth. cbor is nice because it's self describing so you can still understand it without a schema, which is a nice property people like about json.
I haven't used it, but I thought that was the big claim.