Systematic Risk (or Market Risk) is the risk that cannot be avoided and is inherent within the overall market (aka non-diversifiable). Non-Systematic Risk is risk that is local or limited to an asset or industry and investors are capable of avoiding non-systematic risk.
This can be done through diversification by combining non-highly correlated assets. This is also known as idiosyncratic risk.
Investors do not receive any additional returns for bearing more non-systematic risk, and it is in the interest of the investor to hold well-diversified portfolios.