What is a domain name?
A domain name is a unique name of up to sixty-seven characters which serves to identify your site on the internet (explaining how it does that is another days work!)
Any domain name can be broken down into a couple of parts. The tld or top level domain is the ending of your domain name - for example .com, or .it, or .ie, or .biz etc. The tld's are defined by IANA (The Internet Assigned Numbers Authority). A full current list is available here. From time to time new tld's are introduced to answer the requirements of a growing market - for example the proposed .eu tld, or the .mobi
A full domain name is, then, made up of your individual name combined with the top level domain name - for example www.boduweb.com, where boduweb is our chosen name in the top level domain .com.
The existence of a multitude of top level domain names leads to a very obvious problem - the existence of similar but unique names exploiting the range of tld's. So, while we have registered the unique domain name boduweb.com - there's nothing to stop someone else registering the equally unique boduweb.info or boduweb.tv
The bright sparks in ICANN have come up with a dispute resolution policy that all accreddited registrars have to sign up to, which supposedly ensures that domain names registered in bad faith, with the intent of exploiting an already existant trading name/trade mark can speedily be transferred to their more rightful owners - causing an end to cyber-squatting. The reality, though, is that many businesses register their name in all available tld formats to prevent confusion.
That's a choice you'll have to make. For our money's worth, the most important thing is that your website has a clear name and is well designed.In which case anyone who has registered variants of your name will most likely lose out in any case.
What about that www. though?
You've probably noticed various sites that mysteriously manage to replace the omnipresent www. with something else, for example hotels.visit-rimini.com. What's that all about? Well, in that case the hotels. section of the name is what's called a subdomain. Given that www. is common to all domain names, it goes without saying that the unique part of any name has to be formed by the combination of the second and third part of the url. That means that you can pretty much at will put anything into your subdomain, without anyone giving a care. Subdomains don't need to be officially registered, and can be set up at the server level.
The jury is out about how important subdomains are for search engines - but they certainly play some role, so they're something to think about, after you've organised your actual unique and registered domain name.