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A risk premium is the minimum difference between the expected value of an uncertain bet that a person is willing to take and the certain value that he is indifferent to.
Here is a short example to help you get the hang of it. Let's say that you are on a game show where you have the opportunity to choose between two doors, one that has $1000 behind it, and one that has $0 behind it. The game show host also gives you the opportunity to take $500 instead of choosing between the two doors. Both of these options have the same expected value ($500). If you are risk neutral, then you are indifferent (don't care) between these two choices. However, most people are risk averse and would prefer the $500 for sure. This means that the game show host would have to sweeten the deal in the uncertain bet to get people to choose it. Maybe if the host offered $2000 behind the good door and nothing behind the bad door (expected value of $1000) people would accept the gamble. If this were the minimum amount that they would accept (ie they would refuse the bet with $1999 behind the good door), then the risk premium is $500 ($1000-$500).
See the list of economics topics
fr:Prime de risque
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