How to constantly read a sensor value in the background while doing other action

I'm using an ultrasonic sensor and it's basically as long as the sensor value is below a certain threshhold, run the motors. So how can I program the Arduino to constantly read values from the sensor and check if it's passed the threshhold or not in the background? Does this have something to do with interrupts?

Not necessarily interrupts, in fact seldom. All you need to do is make all the code in the loop() function non-blocking, i.e. never waits for very long. Then loop() is executed repeatedly at high speed and everything appears to run "at the same time".

It is a well known and widely used approach, which everyone here will be glad to help you implement. It is important that your ultrasonic code play nicely with this method. That would depend on the library you have, unless you wrote it yourself.

Have a look at this thread with example code for doing several things at once:
Demonstration code for several things at the same time - Project Guidance - Arduino Forum

That is a definitely a great "how to" !!!

Also, I personally learned quite a few things by reading this one as well :

http://forum.arduino.cc/index.php?topic=261445.0

dan