In an age where there are multiple devices, and multiple Internet connections, it’s tough to sync up all of your devices at all times. And truthfully, there shouldn’t be a need for sync your devices every single time.
What Weave does is very similar to the now discontinued Google Browser Sync. Given a database area to store preferences, passwords, history, bookmarks, and other customizations, you can basically load whatever browser preferences are to any device. Currently, this is a closed beta service that will be hosted by Mozilla and if it works out, it’ll definitely be a great replacement for browser services.