I am new to Ubuntu. How is installing software from a repository different from downloading the .deb file from a website and installing through the package manager?
All the other answers are correct, you get:
But most importantly, you get reliability. Repositories systems in place to make sure that the software you download will work on your computer. In windows when you want to install an application to fix a problem, you have to trust not only the website that's hosting it, but all the computers in between.
With key signing, you can be sure that you are installing software that the developers intended for you to install.
That just leaves the issues to you, to make sure that you chose good developers.
