In a “long range attack” on the Ethereum blockchain, like with a 51% attack, an attacher would make a longer chain that “rewrote” the ledger in the their favour. But instead of starting the attack only a few blocks back, the attacker would go back to a point tens of thousands of blocks back where they had a large stake in the network, and start forging blocks such that when they arrive at the height of the main chain, they would hold a large amount of the ether and take over the chain. An attack using a branch that contains different transactions and blocks to overtake the main chain is also referred to as an “Alternative History” or “History Revision” attack.
A 51% attack could start with an attacker who holds 1% of all coins shortly after the genesis block, start their own chain in secret and make it longer than the consensus chain, and then use the next chance they when chosen as a validator to launch their own chain. The time required to accelerate a simulation through a couple years and produce such an false chain is only a couple of minutes. This “costless simulation” and other PoS vulnerabilities such as weak subjectivity make long range attacks potentially more dangerous for PoS compared with PoW.
Casper provides protocols such as Slasher to prevent long range attacks by, for example, timestamping every block so that clients can reject chains with timestamps that are far ahead of their own.
A complete discussion of various types of long range attacks and their solutions can be found here.