Kenyon and its providers never store your password. Kenyon does not know your password and it cannot find that password anywhere. Instead, something called cryptographic hashing is used.
When you create a new password, your computer executes something called a "hashing" on your password. A hashing is a complex mathematical function that alters the text in a single direction. It is very difficult and computationally expensive to undo a hashing, bordering on impossible for modern hashing algorithms. For example, the word `Kenyon` might be hashed into 0af0578e6c1840fd6b532f8ba3e62efd1298ac33. Changing just one letter changes the entire hash: the word `kenyon` is hashed into 463085bf65663dc8da2f390771235184fd0302c6. (Details for nerds: the hash used here is SHA1. Comparatively speaking, it is a weak hashing algorithm, but we're using it for the sake of example.)
When you type in your password to authenticate to a service, like Shibboleth, the hash is regenerated by what you type in. If the hash that is generated matches the hash on file, the authentication is good. If the hashes are at all different, the authentication is no good.
The hash is what is stored by Kenyon or its providers, not your password. Furthermore, this hash, along with the rest of your data, is encrypted using industry-standard encryption standards like AES-256.