A few account settings exist specifically to help you keep your account secure — see Account → Account Settings.
Every account's address is proved with a 6-digit emailed code before it's attached to the account — at sign-up, and again whenever you change it. Changing it also requires your current password, and both the old and new addresses are notified once it goes through. Full details in Email and alerts.
Fill in your current password plus the new one (twice, to confirm) under Change password. You'll need your current password even if you're already logged in. Changing it signs out every other session and sends a notice to your email address.
Scramble Token generates you a brand-new session token and invalidates every other active session for your account — every other browser/device you're logged in on gets signed out, except the one you just clicked the button from. Use this if you suspect a session of yours (a shared computer, an old device, a leaked cookie) might be compromised.
To prevent accidental lockouts from repeated use, you can only scramble your token once every 30 minutes — the button stays disabled with a countdown until you can again.
Log out ends your current session only, leaving any other logged-in sessions untouched. If you want to end all sessions, use Scramble Token instead.
See also: Your Account, Email and alerts.