Page name is a term for the title of any page on Wikipedia. A page is named for the convenience of linking to it by its title. It is shown on the title line, near the top, in large bold letters.
On Wikipedia, a database stores all the pages, and so a page is also named for the convenience of a database query to get that page. In the case of encyclopedic articles, the page name is simply the topic of the article. For other pages, such as those used for administration, the page name will include a topic and a namespace. Talk pages are also stored in the database, and their page names will add the word "talk" to the corresponding page names of their subjects.
A page name on Wikimedia projects differs from most web pages, in that the title can always be interpreted from the URL (except for most pages of Wikidata). A web page URL is more similar to a file name, which can be given any chosen title within the rules. Page name is also different from file name because whereas "file name" and "filename" mean the same thing, "page name" and "pagename" do not always mean the same thing. But pagename is very similar in meaning to "web page title" in that both terms reference the title of a subject, which is a variable for a given author.
Wikipedia has a lot of material to organize; and although the main purpose is the content of articles, most of the pages on Wikipedia are actually organizational and administrative in nature. Just as the title of any document indicates the precise topic that the subject material covers, so an operative page name on Wikipedia indicates which department it serves. A "page name" is just how things work here, to title, link and transclude any page.
So in fact most pages on Wikipedia have a page name with the form Namespace:Pagename, where Pagename (without a middle space) is simply the subject, and obviously different to page name (with a middle space). And the Namespace is the department the page belongs to, which are described at Wikipedia:Namespace. Adding a namespace to a page name enables subject material to focus into two different topics, each having its own audience. A topic is a narrowed, or focused, subject.
For example, Linking is a subject of two page names, one at Help:Linking, which is in the Help namespace, and is for beginner editors; and the other at Wikipedia:Linking, which is in the Wikipedia namespace, and is for more advanced editors. The namespace "Wikipedia" is for more advanced editors, like the administrators of Wikipedia.
Every single page name on Wikipedia has one other aspect beside the subject and the namespace, and that is its talk page. Each talk page also has the word "talk" added to its page name. The audience for any one talk page is concerned about the content of the related topic page. The guidelines of a talk page are described at Wikipedia:Talk page guidelines. Talk pages for a particular namespace as a whole may tend towards a shared style.
The content of articles is Wikipedia's main purpose. There is no technical, proper name for the namespace of articles, but its common name is variously "Main namespace", "Article namespace", "Mainspace" or "Articlespace". Articles are so obviously the main reason for Wikipedia in the first place, that a visible namespace doesn't exist, and there is no mention of it in article titles or links.
The topic for a page is also called the pagename or basename. Some examples:
The term for the Main or the Template namespace conveniently defaults to what is obviously the main reason for the namespace. For example, we can link
[[An article title]], but to transclude it we write
((:An article title)). The ":" character is not part of any namespace name, but here it is as close to the mainspace name as possible.
The namespace for an article is a default that is not technically writable in the page name. Although it is not technically necessary to write "Template" in the page name for a transclusion that achieves the text processing power of template code, it remains true that the markup for transclusion is "a page name in double curly brackets".
Any page on Wikipedia can be wiki-linked to any other using exactly the title. This convenience requires us to prefix the namespace word even if it's a page in the namespace we are working in, unless it's Main. If you stay editing only "content" in "articles", it might seem you can forget about the namespace word in links and titles. That would be true only if only you could discuss on the talk page without making a link to the Wikipedia operational aspects. This is almost certainly impossible, because the Five Pillars of Wikipedia are not in the main namespace. The complication of a namespace was minimized, but it is not gone.
The good news is that there is one way to link that can guarantee error-free linking in all cases: render the target page, use the "copy and paste" operation from the title line of the target page, and use that for your own page. Some of the page names you will find the need to link to in discussion will be policy, guidelines, templates, and the other namespace names. So because the namespace name is in the title, the link will always work by using the title.