After sending out your resume out to every available position, you may get a response from a potential employer. Err, hold on. Wrong "Interview" page, sorry.
Here we are. As you probably have figured out from playing the game, there is an Interview option before each mission begins. After saving, select Interview to jump to the Interview screen, where Bastion can talk to his party members 3 times (you can talk 3 times before you run out of time and the option becomes unavailable until next mission.) Talking to characters boosts their morale, and you get to hear their thoughts, feelings and opinions on how the quest is going so far.
But why bother, you say? Because two of the game's branches have different endings depending on your Morale value, and thus this screen becomes important. Morale can also be changed in battle, where it's lowered if the character is KO'ed or doesn't participate much in battle. Also, morale can sometimes be changed during story scenes in which you choose an option; generally, saying what your team members want to hear boosts morale up.
Here is a sample picture of the Interview screen.
See the little funny faces and the names? Well, here's what that all means. The characters are represented by their sprites up on the top part of the screen; and the row on the left represents the characters and how they feel towards them. For example, take a look at Andrew's sprite (the handsome one, 6th from the left), and follow the row across to Bastion. See that happy face? That means Andrew has a pretty good relationship with Bastion, in a completely platonic way, of course! Now follow Bastion's sprite to Andrew's name.. see?
Now, to improve Bastion's feelings towards someone, you move the cursor over to them and press "X" to talk to them. This will raise Bastion's feelings for them by 2 points. You can talk to the same person three times if you wish, if you're concentrating on relations with one person. Note that the relationships between your characters don't really matter, your team's morale is determined by how your team likes Bastion, and how Bastion likes his team.
Please note, and this is very important, that not everyone will be on your final team, and thus the ending morale for them does not matter. Therefore, know what your final team will be beforehand, and don't bother talking to them. The below chart shows a list of all the team members you can Interview, as well has how much their Morale will go up when you talk to them, and which branches you will have them at the end for.
By the way, each funny little face represents a specific morale point value, ranging from 127 to -128. Below is another handy chart, this time outlining what face means what. Exact point values can't be found, so you'll just have to take a guess.
Now that you understand morale fully, let's look at the two situations where morale is measured.