What do jet pilots say during the takeoff as they are speeding down the runway?
What you are hearing is &quot;V-One&quot;, written as V1.
It actually is said when they can no longer safely abort the takeoff with the remaining runway, but they still are not quite ready to takeoff.
As they get a little faster, there should then be a second callout of &quot;Rotate&quot; when they have achieved the required takeoff speed, and that is when they actually takeoff.
To answer the &quot;why&quot; part, it is said by the pilot who isn't actually flying the airplane since he has more time to monitor the speed and can say it at exactly the right time.  It alerts the other pilot that it is no longer safe to abort the takeoff and that pretty much no matter what happens now, they should continue and come back to land if needed.
Edit:
In my answer above, I simplified somewhat by only mentioning the available runway.  There are other factors that can come into play even with a runway that is longer than needed.  One example would be the speed after which the brakes can no longer stop the airplane because they would over-heat and become ineffective.  This is known as the brake energy limit, and it is not safe to abort above this speed, even if you have &quot;plenty&quot; of runway.
V1 must be calculated or looked up prior to every takeoff, along with the other performance numbers.  They vary based on the weight of the aircraft, the configuration of the aircraft, the altitude of the runway, and the weather (outside temperature, wind, etc.).  Sometimes this is done via a computer and sometimes manually via lookup tables or even graphs.
For an example of the graphs, and more information about how temperature and altitude affect takeoff performance, see my previous answer here:
Does temperature affect takeoff performance?
There are also times when a pilot may increase or decrease V1 intentionally, even when it is not required.  For instance, if there is wet ice on the runway it may not be safe to abort even at a very low speed, so you would be forced to continue no matter what (note that I'm NOT saying that this is a good idea). Using a lower power setting to extend engine life is another example, and you can read about it in my question here:
Why would an airplane pilot choose to intentionally use more runway than required for a takeoff?
For way more information than you probably care about takeoff performance, see my other answer here:
Minimum Runway Length and V1
In closing, aircraft performance planning is a rather complicated subject and it is only one of many subjects that we must master in order to safely fly an airplane.  This only just scratches the surface of it, and there is a lot more that must be considered (such as &quot;hey, will we be able to out-climb that tree off the end of the runway?&quot;).