First seen rule
The first seen rule is a rule that is part of the evaluation criteria of both blocks and transactions on the network.
First seen rule for Blocks
When evaluating blocks, a node considers the first seen block to be the first block that was broadcast which is is able to completely validate which is the furthest from the genesis block in a valid chain of proof of work.
When two blocks are competing in an orphan race, and a node is trying to build upon one of them, if a new block is discovered upon the competitor the node will stop working on the block it saw first and move to the longest chain.
First seen rule for Transactions
When receiving transactions, the first seen rule is applied to determine which transaction is valid in the case of a double spend. When a node detects a double spend, it always considers the transaction that it received first as the valid spender of that coin.
The rule has been extended further to add that any blocks which are discovered that include the double spend transaction that those blocks should also be considered invalid, and that the node should continue to mine against it unless a second block is discovered on top of that block, indicating that a majority of the network has determined that the other transaction was the first seen.