Market risk is the risk of the investor losing his money because of market- or economy-related factors, like political uncertainty, global slowdown, interest rate change.
Market risk is also known as systematic risk. These are the risks which affect the entire economy, and macroeconomic conditions. It is the opposite of unsystematic risk, which is a company-specific risk.
The best way to handle market risk in a portfolio is to hedge against the risk drivers.
For example, a portfolio heavily invested in airline stocks has oil cost as its major risk driver. Hedging against oil price rise would offset market risk.