jsenc is mostly patches and extensions to CryptoJS and also some test scripts to provide demos for their usage. For more info please see the GitHub repository or the index page.
All the cryptographic work (password hashing, data encryption/decryption) is done in your browser, no data is ever transmitted to a server, all the encryption/decryption is happening in this window. This is the exact point of the library. After the page loads you can actually go offline and the page will still work.
About the example
This example provides the following:
text (or arbitary data) encryption using AES
key derivation from a password
SHA256 password hashing with configurable iterations
SHA256 password hashing with configurable salt
configurable AES IV (initialization vector)
JSON output of the encrypted data and parameters, but the password is not included