In short, risk is the probability that an unwanted or unforeseen event will occur during the life cycle of a project. A more precise definition of risk, is the probability and magnitude of unforeseen events. Risk is important in project management because actualized risks can cost lots of money, resources and time. They can bury an otherwise valuable project - sometimes for good.
Risk management is the process of identifying, assessing and planning to work around risks. It is an extremely important part of the project planning process. While risk assessment can take time, it pays for itself in the end by allowing for project managers to foresee potential risks and plan how to combat them even before the project takes off from the ground. Risk assessment and management is like those important tests that pilots must go through before they take off down the runway. It prevents disaster.