The Hundred Schools of Thought refers to a period of the Spring, Autumn and Warring States when different "schools" of thought competed with each other to inform the Chinese people and leaders. To understand the political turmoil of the Warring States Period it is helpful to understand the the intellectual and culture turmoil that society was going through at the time. In turn, this helps understand what lessons the modern CCP leadership are learning from the Warring States Period.
Hundred Schools of Thought - Wikipedia
As with many new fields of study, it is helpful to start with Wikipedia to become familiar with the subject and see the sources that influenced the post. Wikipedia's page does a not job of introducing into the subject.
The Hundred Schools of Thought were philosophies and schools that flourished from the 6th century BC to 221 BC during the Spring and Autumn period and the Warring States period of ancient China.
An era of great cultural and intellectual expansion in China, it was fraught with chaos and bloody battles, but it was also known as the Golden Age of Chinese philosophy because a broad range of thoughts and ideas were developed and discussed freely. This phenomenon has been called the Contention of a Hundred Schools of Thought. The thoughts and ideas discussed and refined during this period have profoundly influenced lifestyles and social consciousness up to the present day in East Asian countries and the East Asian diaspora around the world. The intellectual society of this era was characterized by itinerant scholars, who were often employed by various state rulers as advisers on the methods of government, war, and diplomacy.
This period ended with the rise of the imperial Qin dynasty and the subsequent purge of dissent. (I removed the Chinese text, footnotes and links from this quote)
For more follow this link to the Wikipedia page.
The Philosophical Struggle That Defined China - Hundred Schools of Thought
This is a great video series by the same gentlemen I cited earlier on the Warring States page. He does a very good job of giving an overview and then going into detail on the main schools.