Sandboxing basically puts a safeguard between the applications you've installed and OS X. It should ensure Mac apps are less likely to damage OS X because it limits the amount of interaction they can do with it. This means that the most critical parts of OS X are protected from infection by apps you install - hopefully meaning less major crashes or fatal errors in OS X itself.
This is an understandable move by Apple. Although Macs are still much more resilient to infection than PC's, as the number of Mac users grow, so will the number of Trojans and viruses aimed at it. Also, the fact that OS X has to use vulnerable plugins such as Java and Flash via browsers such as Firefox and Chrome means that certain backdoor vulnerabilities need to be closed.
There are some potential complications for end users however. For example, if an application needs to establish a connection to the internet or interact with another program, the fact that it's been sandboxed may prevent or complicate this. Of course, if the developer has done their job properly and Apple implement sandboxing correctly within the App Store, it shouldn't be a problem and you should notice no major difference in the functionality of your apps.
For developer's, it's more of a headache. It means more work in specifying exactly what their applications can and can't access. There is also a concern that it will lock both developers and users into the App Store: will OS X eventually only accept apps that have been sandbox approved in the App Store first for security reasons?
But initially at least, it should mean a safer OS X experience, better performing apps and less application conflict issues.