Base-256 allows any byte to be represented as a single character, whereas the popular base-64 encoding requires 2 characters per byte. This means that encrypted messages are much shorter.
This is the ad-supported version of Kryptos, which is why it requires internet access as a permission. The ad-free version does not require any internet access. That being said, if you're working with sensitive data it's always a good idea to disconnect your device from all network access.