OK, let's take this from the top.

(1) The list says: "20 capacity". That means that the front cabin has 20 seats. There are 20 tray tables, arm rests, magazine holders, and so on. This is a physical limit of the airplane and never changes. It does not tell you how many first-class seats are still left for sale.

(2) The list says: "18 booked". There are already 18 people on that flight whose reservations say "first class".

(Some of those 18 people may not have seat assignments, so you may not see exactly 18 first class seats occupied on the flight's seat map.)

(3) The list says: "2 checked in". Checking in for a flight is how you get a boarding pass. You can check in at an airport counter or online at united.com. If you don't check in for a flight you will not get to fly on it.

The "gate agent", the person who stands at an airport gate and scans people's boarding passes and tells them to go onto the airplane, will cancel the trips of everyone who is "booked" but not "checked in" at about 30 minutes before departure, if there is anyone like that. If this happens, this will mean that there are fewer people on the flight whose reservations say "first class". This will mean that there will be more unassigned space in first class, and perhaps some upgrades will happen from the upgrade list.

Only people who are booked in first class will check in in first class. You will never see "checked in: 19, booked: 18".

If you think about (1), (2), and (3) very deliberately, you will notice that there are more seats (20) than people with confirmed reservations (18). That suggests there is probably some room for additional upgrades.

Below these numbers, there is a list with 18 names, including a tick mark that shows that 12 of those names have been upgraded.

This list is apparently a little bit confusing! The list length of 18 means that 18 people on the flight either (a) have gotten an upgrade cleared via the free elite-upgrade process or (b) have checked in, are still in coach, and are eligible for upgrades. This list may grow as more people who are eligible for upgrades check in.

(4) The list shows you that 12 people have check marks and seat assignments next to their name, meaning that they were upgraded.

If you think very carefully you may remember that way at the top of the screen, united.com told you that a total of 18 people had reservations in first class. You know that 12 people were upgraded into first class. The other people in first class bought first class tickets. There are 6 other people whose reservations say "first class". They bought first class tickets.

(5) The list also shows you that there are 6 more passengers on an "upgrade standby list" who do not have check marks next to their name. Those people do not have reservations that say "first class".

Now, let's suppose everyone whose reservation already says "first class" visits united.com and checks in for their flight, which is very likely.

If this happens then united.com will show "capacity: 20", "booked: 18", "checked in: 18".

The airport gate agent will look at this information 30 minutes before departure and they will see that 18 people are allowed to board the plane and go into their first class seats.

Because they know that the plane has 20 seats, only one person may sit in one seat, and only 18 people have first-class boarding passes, they know that there will be some seats which will not have any people in them.

When this happens, the gate agent will print a boarding pass for an unassigned first class seat for the top person on the upgrade list and give it to them. They will keep doing this until there are no seats left to assign.