I'm a coder yet I don't understand much about encryption and certificates and signing. Keybase makes it more accessible to me. If you assume that there's many people like me (I bet there are: non-security obsessed coders, geeks, whatnot), then the existence of Keybase makes these concepts accessible to a larger crowd than before. That's a win.
Basically, it works like this (for example, with browser extension client):
1) the client generates a symmetric AES-256 key and uses that to encrypt the email locally
2) Gmail traffics the email to recipients normally, except the body of the email is now encrypted before it even leaves the client (the body also includes the unique id of the key, unencrypted)
3) the key is sent to a third party key store (Virtru) which controls access to the key based on identity (OAuth/OpenID)
https://www.virtru.com/what-is-virtru
It could be interesting to do some type of mash-up with Virtru and Keybase.io so that Virtru could automatically pull recipients' public keys and use a PGP type flow as opposed to the default of a symmetric key.
Happy to answer questions if anyone gives Virtru a try.
So, in other words, keybase could be a valuable and important step toward a "mom friendly" system, but it's a bit early to say.
The other target userbase is people who want to verify GPG keys that don't have a web of trust. This is useful for, say, me - I'm not part of the Debian dev team or anything, so I don't have many people around who can sign my GPG key. It's nice to be able to publish a link to Keybase on my website and have people be able to be pretty sure it's me.