Systemic Risk is a risk due to the daily fluctuation of asset prices or external market factors. Also referred to as market risk. For example, stocks generally do well during bull runs and perform negatively during bear runs. Systemic Risk is something that cannot usually be mitigated (it is built into the system).
Unsystematic Risk is a risk specific to the company or investment. It can be eliminated or reduced through risk management strategies such as diversification. Examples include a product recall at a company or the emergence of a competitor.