A Package Manager is a piece of software that automates the downland and install process for other software. Many operating systems (and some applications!) come with their own package managers. Other operating systems have third party package managers that can be easily installed and drastically expedite and simplify your install processes.
A great package manager for OS X is homebrew. You can install it by typing:
/usr/bin/ruby -e "$(curl -fsSL https://raw.githubusercontent.com/Homebrew/install/master/install)"
into your terminal (/Applications/Utilities/Terminal.app).
Windows Package Managers
There are several package managers available for windows. Windows 10 includes a package manager called oneget. There is a great article for setting up oneget here.
Other Package Managers
Linux comes in many variants. Most variants include their own package manager. The package manager for Debian one of the oldest variants of Linux, is called apt-get. Some other very popular package managers are yum, rpm, pacman, and portage.
Some languages have a package manager as well. Ruby’s package manager is called gem. Node’s package manager is called npm. Python’s package manager is called pip, or, if you are using Python3, pip3.