You are about to share your ©Instapaper account to another web application.
If this site is malevolent, it could use your account to do things on your behalf without your consent (e.g. delete your articles, add spam articles).
Now here are reasons not to worry yourself about that security breach (beside that I could tell you that I'm an honnest guy who wouldn't break into a safe even if I was given the key):
That being said, your password isn't stored in the web app. It is encoded in a cookie stored in your browser.