Reproducible builds refers to the process where a binary/package can be verified that it been built from a specific commit (for example). If the build process is reproducible, it means that every time you build the project, the output is always the same (idempotent). So Signal can publish a binary + a hash + which commit it been built from, and you should be able to checkout that commit, build the project, and once built, both binaries should be exactly the same (the hash for both should be the same).

Not only helpful in being able to verify that the binaries people publish are without 3rd part modifications, but also helpful in debugging and some other scenarios. More info here: https://reproducible-builds.org/

Although, on iOS I think reproducible builds are mostly useless (for the use case of verifying the binaries) as you can't download the binary straight from the App Store nor can you inspect installed binaries on your iPhone (AFAIK).