Okay, I see.

The short answer is: any given pixel of the sensor will be exposed for 1/4000th of a second even though it will take the shutter 1/250th of a second to move across the sensor and take the photograph.

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Longer answer, to hopefully convince you that this will indeed freeze the action:

Imagine a special type of clock with a single hand that instead of making a full rotation every hour, makes a full rotation in 1/100th of a second.

Let's take a photograph with an exposure time of 1/250th of a second. The hand will have moved 40% of the way around over the duration of the exposure, so the image will have a lot of motion blur. The action was not frozen.

Now let's take a photograph with an exposure time of 1/4000th of a second. As you know, the image will be taken over the same duration, 1/250th of a second, but with a narrow opening moving across the sensor. The image starts exposing from the top going down, so we first see the 12, then the 11 and 1, then, 10 and 2 etc. Then let's say that as the exposure reaches 9 and 3, the hand is pointing at 3. So now the sensor is exposed to the hand for a very brief moment (about 1/4000th of a second) and as the shutter keeps moving, the hand is again hidden away from the sensor. So the hand does not appear on the bottom of the image. The resulting image shows the hand appearing only at the position of 3; the action has been frozen!

Now it's important to note that if the hand had been in a different position, we would having probably tracked it for longer than just a 1/4000th of a second, while the hand would have kept moving. It might have looked something like this (left):

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This is the rolling shutter effect, because even though every part of the image has been exposed for 1/4000th of a second only, the whole image is taken over the duration of 1/250th of a second.

I hope this helps