There are many advantages to using client/server based technology. one advantage is that you have one location for storage and manipulation of data. You could have many users working with a set of information and they all see the same thing. If one person updates something, everyone else would immediately see that update. Central installation and maintenance of software is another advantage. Instead of going to each person's workstation to install or upgrade the system, only the central server would need to be modified. This can also save costs if you are looking at a server license as opposed to licenses for each individual client. A third advantage is savings on equipment costs. Servers are generally more expensive machines with faster processing speed and large storage capacity. Clients are usually much cheaper desktop or laptop units, but they can run just like the server depending on your configuration.
As with anything, there are disadvantages as well. With central processing, if your server fails and you don't have a working backup server, no one will be able to use the software or data stored on the server. With distributed processing, if one person's machine fails, the rest will still be working. Another failure point would be the network. Client/server systems require a network to connect everything together. A network outage can be worse because redundancy is often built into the server configuration, but isn't often built into the network. A third potential problem can come from the software. If you make a change to the server, the change will apply to everyone meaning that bugs would apply to everyone as well.