From technical point of view it means that if someone decides to rewrite the history of the blockchain he won't be able to include transactions of those who don't take part in the attack, because every transaction contains the id of one of the recent blocks. When Alice sends money to Bob in exchange for something she'll get what she wants only if Bob validates the transaction. And this can happen only if they are both on the same branch.
This won't protect against most attacks because transactions are easy to create. An attacker can create lots of bogus transactions to and from himself to fill up his blocks. In all cryptocurrencies both users must be on the same branch for a transaction to be seen as valid. The problem is that merchants aren't always online. When they come online they will see two forks, how will they know which is the real fork and which is the attack. Under this scheme they won't know, they will see valid transactions occurring on both forks.
Forgers can't forge all branches at once, they are faced with a choice, an attempt to forge more than one branch will lead to their exclusion from one of the clusters.
How are users excluded? Surely this requires consensus, how will that consensus be achieved?