What is an “invited submission” to a journal? The website of the journal Philosophy and Phenomenological Research says:


  This site only accepts invited submissions.


In general, what is an invited submission? Is this how special issues of journals are published? Why would a journal invite submissions? How does publishing as an invited submission look compared to a normal submission?
An invited submission is as the name implies, something which the editors of the journal invited. You have probably seen this kind of invitation email - "we would like to invite you to write something on [this topic]. Are you interested?"

It may or may not be related to special issues. Special issues are entire issues formed around that single topic (or conference). If the journal is inviting for a special issue, it will say so in the invitation - "we are publishing this special issue and you're an expert on the topic, so we would like to invite you ...". However it's also possible to be invited for regular issues.

A journal invites submissions for several reasons:


If the journal can get big names to write for them, it raises the profile of the journal as well as (hopefully) generates citations. Other researchers are more likely to submit if famous researchers also submit to the journal. This is the most important reason.
The journal may lack papers. The big journals may receive more papers than they can publish, but there're also a lot of small journals that struggle to fill their issues.
The journal may want to expand. This could be its author pool (invite people who've never published in the journal before), its author country pool (invite people from countries who rarely publish in the journal), or its issue count (increase in issue count is a reason to charge higher subscription prices).


Finally, in principle, invited submissions are more prestigious than regular submissions. That's because the author can safely say that someone out there thinks they're an expert in the field. It's especially good if the invitation comes from a famous researcher. However: many poor-quality journals will also resort to invitations to solicit papers. Their aim is merely to get papers, and they don't really care who is writing or even what topic the paper is on. You will have to use your judgment. In my experience, a personalized email coming from an established researcher in your field is the best kind of invitation.