The higher the aperture, the greater the depth of field, or the greater the distance the objects in the shot will be in focus. So, for instance at f/4, you get things in focus at roughly 4x the focal distance. But at say f/11, you get everything in focus at 11x the focal distance. Make sense?
The other numbers you're talking about (1/50 and 1/1.3) are shutter speed, or how long the shutter actually stays open when you activate it. The lower the number (1/50) the faster the shutter will open & close. The higher the number (1/1.3) the slower it will activate. So at 1/50, the shutter only stays open for 1/50th of a second, but at 1/1.3, it stays open for just under a second, which means that the 1/50th is much faster.
Here are a couple examples of DoF for you to consider. And I'm by no means a professional, but you can see that in the first pic, only what's really close is in focus and everything else is blurred. In the 2nd picture, because I used a higher aperture, things that are further away are in focus as well.
Aperture set @ f/2 and shutter speed @ 1/800
Aperture set @ f/4 and shutter speed @ 1/13