From Traderpedia

Definition: The individual in an organization responsible for evaluation of the organization’s exposures to [risk], and controlling these exposures through such means as avoidance or transference (hedging, if and when deemed necessary).

A risk manager at a large hedge fund may be primarily concerned with avoiding excessive exposure to particular currency fluctations, or changes in interest rates. The same role at a trading arcade would instead mean managing the exposures of indvidual traders to ensure they do not exceed their account trading size limits, or expose the firm to losses beyond their account value.