Sequence Proof proves wether a transaction is at a specific position in a sequence. In the context of Rooch, it is used to provide safer transaction confirmation for users.
Without Sequence Proof
In a Layer2 network, limited by Fraud Proof or ZK Proof, the Sequencer can't alter the content of the transaction otherwise it will be facing a slash. However, the Sequencer could reject the transaction from a certain user (by not sending the transaction to DA and Layer1), or change the position of the transaction, to gain indirect profits by colluding with a third party (e.g. rejects a margin deposit transaction in the hope of getting clearance profit, or change transaction order for MEV profit).
With Sequence Proof
With Sequence Proof, once the user submits the transaction to the Sequencer, the Sequencer is required to return a confirmation along with a Sequence Proof proving that the transaction is included in a certain position of a transaction sequence. If later on, the Sequencer removes the transaction from the sequence and doesn't commit it, the user can use the Sequence Proof to arbitrate for slashing the Sequencer.
This mechanism makes sure that the Sequencer is counterincentived for such behaviors and leaves no profit for the Sequencer to gain via rejecting certain transactions.