The little "padlock" symbol means only this:

1. The URL you're surfing to likely starts with "https://" and means you're connected to a site using SSL (secure session layer).

2. The encryption key supplied is working.

That's it. 

There is no assurance that the web site to which you're connected is the bona fide right one. The web site could be bogus, but supplying a perfectly good SSL key. There is no security on any other traffic crossing your network other than the HTTP stream to that website from that browser.

Matter of fact, if you have JavaScript enabled on your browser, you might not be able to assume/infer this much. A malicious website could use JavaScript  to put the padlock icon into your browser and fool you into thinking you're secure when in fact, there is no crypto, there is no SSL, nada. One of my strongest recommendations for people to increase their browser security is to disable JavaScript (in all browsers) and ActiveX (in IE).

In order to secure whole networks and all traffic, there are only two ways that I can suggest it be done:

1. Use L2 (layer 2) hardware crypto on your Ethernet interfaces, switches, bridges, etc.

2. Set up IPSec.

Of these, option (1) is more expensive, but easier to install, manage and use.

IPSec is so fantastically complicated to explain to people unfamiliar with crypto that it is a near-complete failure. If I tried to explain how to set up IPSec to most people here on NAT, they'd be wanting to kill me after a week of frustration and I'd be wishing we never started.