You're asking
What kind of data could be encrypted using javascript?
and Bergi answered that in the comments:
In general, you can encrypt all data that can be represented in binary
That's true, but this is not what you're actually trying to ask. I believe you're looking for scenarios where crypto libraries are useful in the browser. But more on that a little further down.
I believe the encryption of it would be limited to variables of js application and not files on the host
Yes and no. Anything that can be accessed by JavaScript, can be encrypted. Whether this encryption adds any security is a whole other issue. Values that are accessible through variables in JavaScript code can be encrypted. The same goes to user input which includes files that the user explicitly opened in order to upload in a file dialog (example).
Additionally, your JavaScript code has access to the whole file system in Chrome if you really want it.
Here are some scenarios where using Cryptography in JavaScript could make sense, but not all of them are recommended (not exhaustive, but common):
File storage (i.e. Mega) where the symmetric encryption key is never sent to the server but kept on the client or is directly entered by the user. Its security depends on your trust that the service provider doesn't change their own JavaScript and log the key that was used for encryption.
Password-manager (i.e. clipperz) is similar to file storage, but its code is injected to other sites and it must be resilient to not blurt out all its secrets. It can use many different cryptographic primitives.
Poor-man's HTTPS (i.e. too many Stack Overflow questions) where the server has its RSA private key and sends the RSA public key over HTTP (sic!) to the browser. The browser can encrypt any data and send it back to the server (maybe also establishing a symmetric key in the process). The server can decrypt the message with its private key and respond. This is sort-of secure as long as there is no man-in-the-middle attacker that simply injects its own JavaScript that copies any browser data to the attacker's server. SJCL implements ElGamal encryption instead of RSA for this use case.
Hashing data before uploading in order to check for transmission errors or achieve deduplication (no need to upload file, because somebody else already did so). Hashing is technically in the realm of cryptography and many libraries to that.
Online calculators (i.e. my authenticated encryption tests) where valid and easy to use implementations or algorithms can be used directly when implementing the same algorithms in another language. The data is never sent to the server and is encrypted purely in the browser. My "calculator" can be used to test ones own implementation, because it is verified by various test vectors. Others are there to help friends pass hidden messages without proper e-mail encryption.
These should not be done with browser-based crypto:
If you're using only symmetric encryption over HTTP and the exact same key is present at the server and the client, then you have a problem, because the key must be sent in some way for the client to the server or back. If you send the encryption key from the server to the client or the other way around you need to encrypt your symmetric encryption key. The easiest way to do this would be to use TLS. If you use TLS, then the data as well as key are encrypted, so you don't need to encrypt it yourself. This doesn't provide any security, just a little bit of obfuscation. Any passive attacker (observer) can read your messages. You should read: Javascript Cryptography Considered Harmful
Hashing a password for log in is a bad practice. The general consensus is that you need to hash a password many times (PBKDF2, bcrypt, scrypt, Argon2) in order to check whether a user has sent the correct username and password. Some think that if we hash on the client, the password is not sent in the clear over the network and everything is secure. The problem is that if they think that, they are not using HTTPS (which they need). At the same time, the hashed password is their new password. If the server doesn't implement a constant-time comparison, it is trivial to use a timing side-channel attack to log in as any person which you know the username of.
JWT for sessions: Part 1 and part 2