Digital Cameras
Digital cameras have brought features previously available only on high-end cameras to the average photographer. Before digital, amateurs had to make do with no-feature "point and click" cameras or spend large amounts of money and time to buy and learn to use complicated SLR cameras. Setting F-stops, shutter-speed and figuring the correct lighting while trying to focus was hard. Digital cameras, while not necessarily eliminating these things, have automated many functions and made all of them easier to use.
Numerous Pictures
Shooting events with a film camera was a frustrating task. There were only so many frames on a roll of film, multiple settings were hard to configure quickly and images could not be reviewed. Missed shots were the norm. Even the most basic digital camera allows the user to review an image as soon as it is taken. The number of pictures you can take is limited only by the camera's memory. More overall pictures means a better chance of good pictures.
Correct Mistakes
Everybody occasionally takes bad pictures. In the past, many mistakes could not be corrected in developing; often leaving photographers with an "almost great" picture. With digital editing software, correcting these issues is as simple as point and cut and paste. Software can eliminate red-eye (the single biggest issue in pictures), combine two bad images to make a perfect one, paste a better expression on a person's face or totally eliminate an undesired aspect of the photograph.
Add Finishing Touches
Digital software also allows the average photographer to adjust different aspects of a picture without altering the underlying image. At a minimum, the photographer can adjust color, contrast and brightness to make the image better. The photographer can also perform much more complex tasks, such as adjusting tone and lighting or adding washes and fades. If the photographer does not like the result, she can undo everything and try again -- until it is a perfect picture.