The talk is fascinating, and I highly recommend watching it. (It's on YouTube.) It's about 45 minutes long, so enjoy over lunch.
In brief, Moxie cites two problems with the current SSL model, which requires all of us to trust Certificate Authorities (CAs), which have been hacked with increasing frequency, and which have also demonstrated drunk and disorderly behavior at times. One, we have to trust them forever. Two, there is no reasonably way to change who you trust. For example, if one decided that Comodo (one of the largest CAs) just could not be trusted any longer, one could deleted Comodo from his/her browser's "trust database." But doing this would make a large number of Internet web sites (20%) unusable.
Convergence replaces CAs with one or more self-selected "notaries" each of which can use a different method to ascertain whether a certificate is valid, including a self-signed certificate. One may also use a "bounce notary" to separate those that know who you are from those that know where you are browsing.