The basic thing to know about how the sport is played is that the metal ball you see being used is called a shot and that the motion used to move the shot far is not called a throw but rather a put. The shot has different weights depending on the level at which it is being played. The high school and collegiate/Olympic levels have a difference in weight.
Before we get into how the sport works, let's dive into some history about how shot put began. Shot put as we know it today can be tracked all the way back to Scotland in the 1800s in what was known as the Highland Games, where participants would throw a metal weight from behind a line. There are records of the Ancient Greeks throwing stones for sport. Similar to the sport of track and field as a whole, shot put dates back hundreds and hundreds of years. As for its part in the Olympics, shot put has been around since 1896 for men, and 1948 for women.
A fun fact: only three men have ever won back-to-back Olympic titles. And just a few years ago in 2013, Valerie Adams became the first athlete to ever win four consecutive world titles.