The “Change your password” function now has it’s very home—a unique password page. Clicking the “Change password” button will bring you to a standalone page:
When you actually make the changes, you’ll then be prompted to enter your old password (and your 2FA verification code, if applicable) before the changes will be saved:
This helps to ensure that you (and only you, as your password should be yours and yours alone) has the power to make those changes.
UPDATE (10 July 2019): We no longer require 2FA/verification code when making changes to your password.