So those resistors are connected to the inputs on one side(leading to the chip, middle pins on either side are the input lines), and to the power line on the other side.
If you don't know how it works, current likes to take the path of shortest resistance, in this case that's straight from the buttons(that are connected to a positive power line with perhaps a resistor) to the chip's input. BUT, the chip doesn't always 'read' what's on the pin. It has a gate on the other side that gets triggered(opens) by one of the 3 data lines coming from the Teensy. What this means is that there is a floating or uncontrolled voltage between the chip and the button. That's bad, because of induction this voltage floats up and down and will likely cause false data when reading the chip. So what we do in electronics is apply a pull-up or a pull-down resistor.
A pull up resistor usually provides a small current to the line that runs between the chip and the button, so this line will always be HIGH(boolean logical TRUE). With a pull up layout you connect the other side of the button to the ground line, that means when you push down the button all current will drain from the line that the chip is reading and it will read LOW(FALSE), the current coming in through the pull up resistor is not high enough to change the reading, but it will always cause it to stabilize in a single state when you are not operating the button.
there's a bunch of mechanical and inductive effects going on too, but that is not extremely relevant, just keep in mind that a mechanical action like a switch will have a small range where it creates a series of electrical HIGH and LOW states in a very short time when you either press it down or release it. This is called a bounce, and a pull up/pull down resistor is used to counteract this effect. In this case by potential(Voltage at point A exceeds point B, thus it flows from A to B with the difference between them).
A pull down resistor layout works the same, only then we don't connect our resistors to a positive voltage line(source, V+, Vdd etc), but to a negative voltage line(GND, V-, Vcc/Vss, ground plane also). thus reversing the effect.
I hope this explains it a little, I always meander a little when it comes to topics like this!