Signing is a step in the build process where the output file (the binary file of your application) gets a signature generated from a certificate.
This is done to prove the identity of the app's creator and also prove the integrity of the file.
When building Android apps, the signing is done by a self-generated certificate, but when signing iOS apps the signing is done by a certificate generated by Apple which is strictly bound to your Apple account.
Read more about signing for Android here and more about signing for iOS here.