You're reading a webpage now, obviously, but how do they work and what do you need to know about that? There's two basic aspects to it: webpages, and webservers.
Webpages are files written in a manner that can be understood by anything purporting to be a web browser. Generally, they're written in HTML, and most web browsers can do a reasonable job of displaying it, even if some don't manage the finer aspects of it too brilliantly (e.g. Microsoft's “Internet Explorer”).
i.e. You don't need to be using a specific program to read them, you can use whichever one you prefer to. There's a plethora of different web browsers available, for many different types of computer systems. HTML was designed to overcome that age-old computer problem where documents were written in a manner that required you to use the same program to read it as whatever was used to write it—which meant that if you didn't have it you were out of luck, and if your system wasn't set up just like the author's system you got a mess.
Webpages come from a webserver. Your browser connects to its internet address and requests a specific page, like this particular page; or you just connect to the server address without making a request for a specific page, and it gives you its default page (the “homepage”).
It's a bit like going up to a person handing out leaflets in a shopping centre. You approach them, and they give you a leaflet. If they've got different leaflets to hand out, you can get what you ask them for. That person is acting as a “server”, they serve information on request. They have an location that you can find them at (an address), and they have different resources on offer that you can request.
(Webservers can serve more than just “pages”, by the way. The same process is involved whether you request a page, a picture, or some other type of information.)
Taking things a step further, webpages can refer to other resources with a “link”, or “hyperlink”, to another page. When you follow that link (e.g. by clicking on it with a mouse), you get that new resource (your browser asks for it from the server, the server sends it, the browser shows it to you). This new resource could come from the same server, or from a completely different one.
(Link and hyperlink are two names for the same thing.)
And webpages are rarely as simple as just mentioned. They usually include other resources, as well. For example, a page with a couple of pictures on it is made from three resources: the written content, and the two pictures (i.e. they're all individual items). You request the page, and it refers to the included objects, and your browser assembles them together, as best it can, according to how the page is written.
This (that the items that go together in a page are actually separate things) might help you understand how some pages can fail to work properly, yet not fail completely. For example, if the page has an error in it, it might only work partially; or if there's an error with the images, the page can work without them.
Webpage addresses are constructed in a uniform manner, properly known as an Uniform Resource Indicator (URI), or Uniform Resource Locator (URL). Either the term URI or URL can be used, though URI is more correct, and the non-technical description of “webpage address” should be understood by anyone hearing it mentioned.
What all of that “uniform” business refers to is a standard, consistent, way of writing addresses. It starts with the protocol used to access the page (HTTP, written as “http://”), the server's host address (e.g. www.example.com), and can be followed with a request for a specific resource that's on that server (e.g. help.html).
You can recognise a webpage address, as being one, if it's written in this manner. If it's not written properly it's ambiguous, and may not be one (there's quite a few similar looking internet addresses with quite different purposes.
The prefixing protocol (i.e. http://) is a mandatory part of the address, however many web browsers will presume it if you don't bother to type it in, and change what you typed in to include it. But if you omit it, and the browser doesn't fix it for you, type it in yourself.
The “www.” hostname prefix is entirely arbitrary, and not enough to identify an address as being for a webpage. Other non-webpage things can use a “www.” prefixed address, and webpages can have non “www.” prefixed addresses.
Cookies are an exchange of data between your browser and the webserver, with the difference being that some information can be stored on your computer for use later on by the webserver (while browsing the site for the current session, or stored for use with another browsing session). It's rather like having your hand stamped when you go around a convention, everyone there can tell where you've been, and treat you differently because of it.
In some cases their use is benign, they can help you use a website in a more useful way. But they're often just there for the website's interests (tracking what you do), and frequently are abused (tracking what you do between different websites, for their own nefarious purposes).
Many browsers come preset to ask you about cookies, but after lots of warnings people generally get sick of them and turn off the warnings (which usually means that all cookies are accepted silently, not rejected silently).
A problem with blandly allowing cookies without checking is that you don't know when the information is being spread around. You might like the convenience of your web browser automatically logging you in the next time you visit, but maybe you'd like to log in anonymously at times, or you don't want everything that you look at on that website (or other sites) associated with your personal details. But unless your browser asks you to allow the cookie, you won't know that it's doing that.
Conversely, if you rely on the cookies to keep on using some website, then you try to use it on another computer, you mightn't be able to remember your passwords, as you've not had to keep on typing them in.
You'll have to decide for yourself what's more important, your privacy or being able to use some website that insists on them (NB: You probably can find out the same information from some other website that doesn't want to exploit you).
Scripts are programs that run on your computer, at the whim of whoever wrote them into their webpage. They can do neat tricks, and they can also do some quite nasty tricks. Don't believe the duff warning that Microsoft's Internet Explorer tells you about most scripts being safe, it's not telling you that this script might be safe because it's checked what it does, it issues the same warning for any script.
JavaScript, ActiveX, VBS, Java, and a few other programing languages that can be run in your web browser are different ways of making pages more interactive or showy (straight HTML is just text to display, images to show, and links to follow). They all have the good and bad sides, though VBS and ActiveX would have to be the most riskiest things to allow (there's almost no limit to what they can do to your computer).
Few useful websites require you to allow them to run, it tends to be only the written-by-idiots websites that insist on them, and it can easily be a written-to-attack you website that includes them. Try not allowing them and see if the site works for you. If the site fails without them think about whether you really need to use that particular site.