Wireless networks provide two things: Mobility and cost savings.
Many companies want the ability to move around the office with their laptops and provide visitors with easy access to the internet as a convenience offering. A wireless network provides both of these things without the need for putting network cabling everywhere and requiring that computers be cabled directly to a jack.
The cost of a wireless router is well below $100 with enterprise solutions being somewhat higher. Enterprise wireless solutions provide more features like password authentication, guest access, terms of use acceptance, and more. On the other hand, wired cable jacks can run anywhere from $50-$100 or more for each location.
So you can see that wireless can save significant expense. It is also possible to run printers and other devices wirelessly as well saving the headache of running a special cable just for them. However, I do not necessarily recommend going with a wireless only solution either. Phone systems are moving quickly towards Voice Over IP (VoIP) and I have not seen an adequate wireless desk phone plus the inherent instability of wireless networks makes a cabled VoIP phone preferable. Also, most printers and of course fax machines still need to be cabled directly to the network.
Wireless security has always been a concern. I would never recommend setting a wireless network up straight out of the box without securing it. But the current models all have straightforward configuration routines to easily configure adequate security for most business settings.
Interference is the main downside to a wireless network. Other electronic devices can cause interference especially things like microwave ovens and other wireless networks. Sold walls, concrete, brick and other building features can reduce the signal strength and the distance the network can reach.
For the cost and convenience most small office networks are adding wireless capability. Just make sure you secure the device and position in physically so it gets the greatest coverage with the minimal amount of interference.