As Garry says, they're applications that install and remove software from Ubuntu's software repositories, amongst other tasks. If you've no idea what that means, let's step back one further:
- Software (like Firefox, GIMP, xchat, etc) is compiled and then packaged into
- These debs are essentially installers. They contain all the files that get copied into the system as well as scripts that allow it to depend on (or conflict with) other known packages.
- If you install Firefox from a package, apt and dpkg (the applications that processes the dependencies) will make sure you have its dependencies installed first and if you haven't, it'll grab those packages too.
- Packages are stored in online repositories as big lists.
- Apt is the tool (or set of tools) that downloads all these lists from various sources, combines them and allows you to select certain packages for installation.
- The benefit to all this is you can install a lot of software without having to hunt for it. More than that, the software in the official Ubuntu repositories is maintained so that if security fixes are released, they're applied and a new package is created. When apt next checks for updates, it sees the new version and you're prompted to download it.
I won't say apt-get/aptitude are useless because they're not, they're both very powerful utilities and like a lot of CLI-vs-GUI comparisons, if you know how to use them, they're a good deal faster than the Software Center.
But punching in random commands without knowing what to expect is a recipe for disaster. It only takes one bad/clumsey person to suggest a destructive command and you'll nuke your system. If you don't know what something's going to do either:
man <command> (eg
man apt-get) to see the manual page for a specific application.
The command line in Linux systems is a good few hundred thousand times more powerful than it's Windows counterpart. You have to treat it with respect or it will bite your legs off.