According to Allegro, the 3144 has been out of production for a while, but does have a replacement...
Anyhow, I assume by the directly plugging in refers to something like a motor controller with hall effect sensor inputs. That's not what you have. When the output of this sensor turns on, it will pull the output pin to ground. Otherwise, it will tend to float. That's why you need the pull-up. That's just a resistor to the Arduino's 5V pin; I usually use 1K but it's probably not critical.
Arduino pins have built-in pullups that are under program control. You turn them on by setting the pinMode to INPUT and then writing the pin HIGH.