Reading:
view - Your web site - what you need
view - Your web site - drawing up a specification
What can an 'active' web site do for you?
view - Database-driven websites
view - Hidden 'extras' of e-commerce
view - E-commerce on the cheap

What is an 'active' site?

We use the term 'active' to refer to any elements of a website that are not 'static', regardless of the technology that makes them work.
Static pages are those with just graphics and text.
An active page/site can range from the trivial to very sophisticated. It might not appear that way to the viewer. In fact, it should never appear complicated to the viewer no matter what level of complexity is tunning behind the scenes.

Activity
So an active page might just consist of 'roll-over' navigational buttons run by javascript.
Or it could be a map where regions highlight as the mouse is passed over them, with explanatory text on each region appearing underneath.
At the basic level, a form on the page can be formatted and emailed to a specified person (for instance, for enrollment application); javascript can be used as another level, to check that the 'name' and 'email' fields have been filled in.
Using more complex scripting languages like ASP and PHP, connections can be made to databases, and data from the form can be stored and manipulated.
A database can also be used to hold information that can be selectively presented to the viewer (for instance a visitor could see their purchase history, but a site-owner could log in at a higher level and see everyone's history, order-status etc)

Edit your own pages
Another use for 'active' sites is to allow the site-owner or an employee to have behind-the-scenes access to page content. This would allow content to be edited, changed and added to without going back to a developer.
The viewer would see none of this 'active' activity. The site would just appear as a (hopefully) regularly updating series of static pages.
So - want to fix up a spelling mistake, or change some pricings, dates etc? With this sort of active component, it becomes a trivial procedure for you, rather than an outside job.

Visitor attractions
You could use an active page to allow visitors to choose from a range of images and send one as an electronic card by email.
Or if you have a fantastic offer, an exclusive interview with the first Martian visitor to Earth, or a compelling ngo initiative, let your visitors send an email directly from the website to friends (assuming they want to know about the first Martian).

Visitor interaction
Of course you may want to create a vibrant community of visitors to your site by offering forums, chat rooms etc.
Again, a database plus some programming, holds all this content, but it is users who are constantly adding to it. The site-owner might have behind-the-scenes access to forum content, so that they can, for example, ban bad users, approve or remove messages, or change the look of the forum.
On a more basic level, you could allow visitors to subscribe to your regular email newsletter, by either sending an email from the page, or entering themselves into your subscriber database.
This database could then be accessed to send the newsletter.

Shopping carts and e-commerce ability are complex 'active' components of a website, but they are really just ways of collecting and storing information about a visitor's purchases. A live-transaction processor adds the ability to check credit card details and put the pransaction through an online bank process.
Hybrid has a shopping cart component that can easily be customised to your website, and your required payment methods, called the HybridCart.