What is it. It is not a romantical thing, sweet spot in photography means the sharpest aperture. For most lenses it is f/5.6, some longer lenses, with a focal length of 300mm, is f/8 or smaller.
Usually every lens starts to get not as sharp from f/8, due to a physical phenomenon called diffraction. It depends on the pixel size of the camera as well. Camera with bigger pixels are usually better.
How to find out where is the sweet spot of your lens?
The very best lenses are giving quite similar quality at all focal lengths, some cheap lenses are where bad usually wide open, after gets better.
If your shutter speed is high enough one of the reason why your images are not sharp, can be that you use your lens at not the best aperture, but perhaps wide open. But you can only be sure after checking.