By entering your Twitter password and clicking "Verify" (for un-verified profiles) or "Login" (for verified profiles), Twellow will be able to ask Twitter if this is really you. Once you have been verified, your username will be marked as having been claimed by you. You will then be able to edit your personal details on Twellow independent of your Twitter account. If you've already been verified, this will log you in. Being logged in will allow you to edit your Twellow profile.
Please note that Twellow does not store or otherwise use your Twitter password. The login is only used to verify your Twitter account ownership.
Twellow Verified profiles are those for which the owner of the profile has successfully verified their ownership. Once a profile is verified, the user can then login and manage their personal data on Twellow.