Your account
An account keeps your scores, your streak and any unfinished set in step across your phone, your tablet and your desktop. The game itself needs nothing: play it signed out, exactly as before.
Signed in as
What an account does, and what it does not
Signed out, everything you play is written to this browser and nowhere else: clear your site data and the record is gone. Signed in, four things follow you instead. Your finished sets land on the account, so a phone and a laptop show the same history. Your streak is counted on the server from the dates you actually played, so switching devices never breaks it. A set left half finished can be picked up where you stopped. And a display name, if you choose one, puts you on the leaderboard.
What it does not do: nothing about the game changes. Sets play identically, offline play still works, and the puzzles are the same for everyone on a given day. The first time you sign in, sets you already played in this browser are moved over to the account, and when the same date was played on both sides the better total is the one kept.