marginal rate of substitution (MRS) is the units of good x have to be given up in order to gain an extra unit of good y, while keeping the same level of utility.
For example, a consumer chooses between hamburgers and hotdogs. In order to determine the marginal rate of substitution, the consumer is asked what combinations of hamburgers and hotdogs provide the same level of satisfaction. When these combinations are graphed, the slope of the resulting line is negative. This means that the consumer faces a diminishing marginal rate of substitution: the more hamburgers they have relative to hotdogs, the fewer hotdogs the consumer is willing to give up for more hamburgers. If the marginal rate of substitution of hamburgers for hot dogs is 2, then the individual would be willing to give up 2 hotdogs in order to obtain 1 extra hamburger.