Mainly convince.
For example, I could be sitting downstairs [internet connection and desktop PC is upstairs] or even in the garden [well in summer!] with my laptop [which sadly is being picked up on Friday to be repaired
]. Wireless, if you set it up right, is easy, and the fastest and most convenient way of setting up a network [aside from the systems that use your house wiring to transport data]. I have never had any problems with wireless apart from a faulty router, which was replaced under the manufacturers lifetime warranty, and I was even allowed to keep the old one.
As for security - I have WPA encryption enabled, and a long password on it. But I'm not too concerned about security, as I've got nothing to hide. And because of my house's location, only one of my neighbors would be able to reach the signal.