The longer you let light in ( 1sec. as compared to 1/2 sec.) the more a moving subject will blur. Like the waterfall. Shorter shutter speed will freeze it. Longer will let it blur. Same with kids.
The f-stop or aperture is how wide the lens is open.
The aperture lets in varying amounts of light. Like shutter speeds, apertures are "stops". That is, changing the aperture 1 stop halves or doubles, the amount of light let into the camera. So going from f5.6 to f4, with all else being the same, the exposure doubles. Going from f5.6 to f8 cuts the exposure in half. The larger the f-stop (lower the number, such as 1.8) the less DOF you have. A smaller f-stop (higher number, such as 16) the more depth you have.
To start out you might try Av mode or Aperture priority. You set the f-stop, the camera will find the right shutter speed. It will give you a good idea of how the depth of field changes with f-stops.
Later switch to Tv or shutter priority to get a better idea of how shutter speed affects your images.
A smaller f-stop (f16-f22) would give you greater DOF for landscapes. Larger f-stop (f3.5-f4) shallower DOF to blur (or de-focus)backgrounds, say activity or distractions behind your children.
Hope that helps. It will all come back in time.
