Wide open in photography means the widest aperture that the lens will give you. This is often around f/4.5 with most lenses. I can go wider with my prime lens which will go to f/1.8. Take a look at this wide open shot of some beer cans:
The focus points on a camera are used to focus on your subject but they are also used for metering. My Nikon D3200 has 11 focus points and they are useful but I often only use one. Some cameras have a lot more focus points and they cover the whole frame.
All digital cameras have focus points, some cameras like my Fujifilm, just have one. My Nikon D3200 has 11 focus points that come up as red dots. It is important to get those focus points on your subject. I like to use one focus point for a single subject such as photographing one person and all 11 focus points for a group or a landscape.