It means that the applicaiton you want to install requires libraries – code – from sources that Ubuntu doesn’t verify.
Imagine you have a car, and you want to upgrade the exhaust system. That might involve the use of parts that are not authorised by the manufacturer of the car. It’s the same principle.
When Software Centre gives you this message, is there any option to go ahead and install all the packages? If there is, and you’re sure you want to, click “yes” or somesuch, and the install will go ahead.
Generally speaking, it’s unlikely to cause a problem if you install the 3rd party libraries. However, Ubuntu is not responsible for maintaining that software, which means that any security issues that arise will be resolved by the producer of the code. This might mean that it never gets updated. Moreover, you might find that you run into compatibility problems down the line some time.
What software do you want to install, if you don’t mind me asking?