My understanding is that "Primary" is the default tab for any conversations (groups of messages) not showing up under the other tabs.
"Social" are messages connected with social media, such as LinkedIn, Facebook, and blogs I've subscribed to, etc.
"Promotions" are messages that have an advertising flavor to them. Promotions are not spam as that goes into the spam filter. A sample message is like the one I got from Toyota today, "Bruce, Get a First Look at the All-New Corolla."
"Updates" are more newsy items from companies that I have a relationship with. A typical entry is from Fidelity Investments, "Tax-smart investing tips."
As I mentioned, I'm training it. For example, the two messages from Cincinnati.com showing in image showed up under "Updates" and I want news like this to be under "Primary." To move them, I selected them with a check in the box at the left then right-clicked (left-clicked for left handers) on the message and selected "Move to Tab ➜" then "Primary". I got a confirmation message that the message had been moved and this:
"Do this for future messages from firstname.lastname@example.org? ".
* Yes, I have 14,435 messages in my Inbox of which 4,868 are unread. Google said when I signed up that I don't have to delete messages any more and I listened to them. I recently searched for and used a message I wrote in 2008.
Earlier this week, I passed a milestone that I like: I have now reached over 1,000 page views on this blog. Someone out there is reading my stuff.