Like your aperture, the shutter speed you set on your camera also controls the amount of light
reaching your digital media. Yes, a "faster shutter speed" will freeze the action in your photo, but
it will also allow less light to reach the digital media.
To continue with the metaphor of the room and the window, if you leave the curtains open for an hour you allow more light (cumulatively) into the room than if you leave them open for half an hour. That’s how your camera’s
shutter speed works as well.. The slower the shutter speed the more light enters the camera, and vice versa.
To reiterate this the faster the shutter speed the less light gets into your camera. Shutter speeds are actually
fractions so the number 250 on your camera is actually 1/250, 4 is 1/4, and 2 is actually 1/2. Back in about fourth
grade we learned that 1/2 is larger than 1/4. With shutter speeds 1/2 allows more light into your camera than 1/4
The smaller the fraction, the "faster" the shutter speed, so 1000 is faster than 250 and allows less light in to
the camera. BTW when talking about shutter speeds talk of them as fractions.  1000 is actually 1/1000 or
one one thousandth of a second.