Total duration assumes the whole curve shifts in parallel, which it almost never does. Key rate durations break the risk into buckets at 2, 5, 10 and 30 years so you can see whether a book is really exposed to the front end or the long end.
Two portfolios can have identical overall duration and opposite outcomes in a curve-steepener. Key rate durations are how you spot that before it costs you.
Example: a barbell of 2-year and 30-year bonds and a single 10-year bond both show duration 7. The barbell has key rate durations of 1.0 at 2 years and 6.0 at 30 years; the 10-year has 7.0 at 10 years. A steepening move hurts one and helps the other.
Related: duration, curve-steepener, curve-flattener, curve-butterfly, dv01