In short, transaction replay offers protection in the event that Bitcoin forks, smartly preserving transactions at the Stacks layer should Bitcoin fork away the block the Stacks block was connected to.
Some background: All Stacks blocks are anchored to a particular Bitcoin block. When Bitcoin forks, the Stacks blocks associated with the old fork, and therefore the transactions in that Stacks block, would be ‘lost’ if there were no logic to handle this situation. This is an important problem because not handling this scenario can result in a sub-par experience for users. For example, miners have the ability to extract MEV by ordering these transactions in a certain way (ie, sandwiching) that can harm users and general confusion about seeing a transaction go through and it ‘disappearing’.
In sum, "Transaction replay" refers to the set of solutions to ensure these transactions, instead of being lost, are ‘replayed’ on the now canonical fork of Bitcoin in a new Stacks block. Typically, Bitcoin does not fork very deeply, and these smaller forks are already handled well by the current system, but these additional transaction replay features offer important additional robustness as the network looks to scale Bitcoin DeFi and other use cases.