It's easier and more comfortable to browse profiles from your bed or dinning room table. There is a chance to meet someone whom you probably never would have met any other way since you may not travel in the same circles. There's a large variety of folks.
If you are getting older there comes a time where you don't want to stand in a long line waiting to get into some over crowded nightclub or sit in a piano lounge looking up at the door every ten minutes to see who walks in.
Also if you are a guy you'll find more women are willing to initiate contact through a dating site with you then they would in a public place.
Online dating also is in many ways a more "pro-active" way to meet someone. It's almost like shopping. However the number one reason is probably because people are too busy or too tired to be running around attending various events in hopes of meeting someone. They'd also rather go online than to deal with another "blind date" arranged by family or friends.