Most modern Unix and Linux distributions have a way to install software. Typically, if you wanted to install software, you would have to download the source code and compile it. When you use a Package Manager, typically you get a pre-compiled binary. This saves you time and effort when installing software.
If you want to install Apache, for example, you would install it using the Package Manager. The Package Manager would then download the latest version from the repo and install it. This also greatly simplifies keeping your software updated.
Different Operating Systems use different Package Managers. In some cases the Package Manager will compile a binary for you, such as with FreeBSD Ports. See below for a list of Package Managers by Distribution. We will continue to update this list as we add more information.