Quantitative trading is defined by Ernest P. Chan in his book Quantitative Trading - How to Build Your Own Algorithmic Trading Business
Definition
Quantitative trading, also known as algorithmic trading, is the trading of securities based strictly on the buy/sell decisions of computer algorithms. The computer algorithms are designed and perhaps programmed by the traders themselves, based on the historical performance of the encoded strategy tested against historical financial data.
source: in Quantitative Trading - How to Build Your Own Algorithmic Trading Business
In simple terms, when we trade stocks or any securities based on computer algorithms its known as quantitative or algorithmic trading