Shutter lag is a digital phenomenon, and refers to the time between the moment that you hit the button to take the picture with your digital camera and the moment that the camera actually captures the image. Lag time used to be much worse in older models but improves with each generation of the new digitals. Still, lag can sometimes feel like an eternity when trying to capture a moment. I've seen children go from laughing to crying in that amount of time!
Film cameras really don't have any lag, but on many digital models (though not the more expensive SLRs), the lag is considerable; enough to mean the difference of capturing the moment and not.
The truth is, as much experimenting as you want to do and as much as you want to spend on equipment, taking pictures is all about capturing a moment. Miss the moment and it doesn't matter what kind of camera you have.
I once went to a friend's to see his wedding pictures. He showed me the pictures shot by a professional using the best camera, flash, lighting system and other equipment. Then he showed me pictures taken by friends and family with disposal cameras and average digital cameras. Though the professional took better quality pictures, the friends caught much better moments.
I'll take a captured moment over quality any time. I recently went to a birthday party with my children. My youngest daughter was having a blast, smile painted on her face. I kept trying to take pictures of her, but when I looked at the screen, all I that was left was an arm or wisp of hair as she had moved away by the time the camera captured (or missed) the moment.
I believe without a doubt the #1 Rule in photography is Get the Shot.
So what to do about this pesky shutter lag problem? Digital cameras work by first pressing the shutter button half way to focus and then fully depressing to take the picture. What you can do is if you know you are getting ready to take a picture is:
1. Turn off all automatic features like red-eye reduction
2. Focus on your subject a couple of seconds before you know you want to take the picture, track the subject, wait for your moment, and then...snap...take the picture and capture the moment forever!