http://www.seci.info/stat/stat2_3.pdf gives a nice depiction.
When doing rate comparison, people want to know how their rate compares with others.
The mean doesn't provide comparative information because it's extremely influenced by outliers. Example: if 9 people make $10K p.a., and one makes $110K, the mean is $200K/10 = $20K. Which most people would find useless for comparison purposes since most of the people in the sample make only half that!
Similarly with the median. It represents the point at which half the values are above and the other half below without regard to what the numbers are, or their "lumpiness". If we take the case where out of 100 people 50 get $10K p.a. and the other 50 all over $100K, will the median be useful for comparison? Not very.
The mode, in contrast, is the "most popular" value. Because it's the one with the greatest number of instances, comparisons are meaningful even if the range of values has more than one mode, as for example the salaries in a law office. If you're being asked to accept $50K p.a. as an associate, and you know that the clerical staff get $35K, the associates get $75K, and the partners get $1M or more, you know that if you take the job you'll be underpaid by comparison with your peers. Neither the mean nor the median can tell you that, but the mode can.