A neuron in your brain and a macrophage in your blood both have the same DNA, yet their shapes, sizes, and functions are vastly different from each other.
The cells in our bodies become structurally and functionally diverse by activating different combinations of genes. By studying the RNA that is transcribed from these genes, we can find out which genes are active in a particular cell type, bringing us closer to understanding how a cell can perform its specialized job. In addition to comparing the expressed (ie. active) genes between different types of cells, we can also study how these patterns of gene expression change over time or in response to different stimuli. Using this information, we can start answering questions like "Why does taking aspirin relieve pain, and how does it cause its side effects?"
In short, examining DNA provides us with a static picture of what a cell or organism might do or become, whereas measuring RNA lets us see what a cell/organism is actually doing right now. None of this is to say sequencing RNA is "better" or more important than sequencing DNA. The truth is these two processes are dependent upon and inform each other.
