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An operation-based synchronizer is a synchronizer which sends just the changes (the "operations") to the server, rather than the whole new state. So if I add a line of text to something, then it would send back a message to the server saying "this line of text was added".

Presumably, a state-based synchronizer sends the entire updated state every time, but I don't know offhand.

See slide #5 onwards of:

http://www.cis.upenn.edu/~bcpierce/papers/harmonyslides-2003...

It explains the terms and explores the pros and cons of each approach.

If I were to guess, I'd say operation based synchronisation is based on syncing user actions and then executing them on the other side to catch up. E.g., user deleted record 23. User added a record with this data. User changed this field to be this new value.

I'm a native english speaker and I have no idea what that means either.