Some transactions are tied to a specific keyword or a set of keywords. Clicking on a transaction line item will expand the transaction and expose the keyword for that transaction (if it has one). Checking this option will ensure that all past and future transactions will automatically get labelled for the category chosen for that transaction.
Example: A transaction from Publix has the keyword 'Publix' and is categorized as 'Groceries'. If the Assign Keyword is checked, all past and future transactions from Publix will be categorized as 'Groceries'.
Changing the category of a checked assign keyword transaction will update all past and future transactions with the newly selected category.