This is all about trust.
Say you visit a popular website that presents a certificate. This is the website saying "This is who I am, you can trust me, because I have this letter of introduction signed by someone you trust."
In this case, the 'someone you trust' is one of the certificate authorties who have, (hopefully) done the leg work in establishing the identity of the presenter of the certificate on your behalf.
What you're really trusting is the browser author's trust in the certificate authority's trust in the identity of the person presenting the certificate. There is also often more than one authority between you and the presenter, hence the term: 'Trust Chain'. 
When you sign your own certificate, there is no trust chain . Your site is presenting your own certificate back to you. If you install your own certificate in your browser as one that you trust, then that is treated as an authority, the same as the ones that come pre-installed. You then have a trust chain with only one link.
If you then visit your of of your own sites and your browser warns you that it is presenting an untrusted certificate, you should then have cause for concern, since, as with any other site that presents an untrusted certificate, you can't be certain that you're communicating with the real site.
Note that I made no mention of encryption, yet. Certificates are about authenticating the identity of the party with whom you are communicating. Through trusted certificates there's a way for you to be reasonably assured that your shop or bank is the real one. Once you've established their identity, securing the communications between you is the next step. It so happens that certificates also contain within them the keys required to facilitate this security. Assuming you've set your SSL up correctly, then this communicaiton is as secure as one you'd have with your shop or bank, and your passwords are equally protected.
 This is by no means a flawless system. A free market and a low-margin, high-volume business inevitably leads to cost-cutting: http://www.theregister.co.uk/2011/04/11/state_of_ssl_analysis/
 At least, protected enough that it's far cheaper for someone to break into your house beat your secrets out of you rather than attempt to crack them: http://xkcd.com/538/