A unique web address, when taking the positioning of a period or periods into account, means that the web address will have only one period - just before the .com or .org or .net or whatever the domain extension is - if the web address has two two or more periods in it, it means that it is only part of another site, and not hosted on a server all on its own. Underscores and dashes can be used in any web address to separate words. If you register a domain for yourself, you will be registering thedomainnameyouchoose.com (for eg) or the-domain-name-you-choose.com or the_domain_name_you_choose.com but not thedomainnameyou.choose.com
You can also only register a domain name if it is not yet taken by somebody else, making your web address unique. However, you could still register thedomainnameofyourchoice.net or .org if the .com one is already taken - as long as there are no brand name copyright infringements.