Accepting risk is acknowledging the possibility of losing some or all of the investment principal. High risk typically means high volatility. When something is high in volatility, it is unpredictably irresolute. Both timing and degree of fluctuation are difficult to anticipate. When something is low in volatility its movements are predictable with a high degree of certainty, it is low risk.
Risk is not independent and should not be considered in a vacuum. Risk generally correlates positively with return. This means that as risk increases, so do potential returns. Unlike other risks we accept, there is no such thing as investment insurance to protect against bad investments.
When considering risk you must weigh the possible gains vs. the possible losses. The degree of risk that someone is willing to accept depends on a number of factors. One is simply personal preference. How much risk can be comfortably tolerated? A second is investment goal: Growth? Capital preservation? Income? A third is time horizon: how much time is there until the funds are required? High risk investments tend to do well over the long-term because time has a way of taming risk. Low risk investments do well in the short-term because they are more predictable and sometimes more liquid. There are many factors in determining acceptable risk; most of them tend to overlap.