Quantitative investing is using primarily quantitative information to justify the investment decision. This is different from an investment process which relies primarily on expert judgement.
Example: when assessing a companies financial reporting quality a quantitative investor may rather run a fraud detection model where a non-quantitative investor may rather judge the reliability, character, opportunity and other factors of the CFO.
Quantitative decision making can be applied not only to trading but also to research, portfolio construction, execution and other investment disciplines.