Depth of processing is the first characteristic of the DOES model that Dr. Aron writes about:
At the foundation of the trait of high sensitivity is the tendency to process information more deeply… HSPs simply process everything more, relating and comparing what they notice to their past experience with other similar things. They do it whether they are aware of it or not. When we decide without knowing how we came to that decision, we call this intuition, and HSPs have good (but not infallible!) intuition. When you make a decision consciously, you may notice that you are slower than others because you think over all the options so carefully. That’s depth of processing too.
Studies supporting the depth of processing aspect of the trait have compared the brain activation of sensitive and non-sensitive people doing various perceptual tasks. Research by Jadzia Jagiellowicz found that the highly sensitive use more of those parts of the brain associated with “deeper” processing of information, especially on tasks that involve noticing subtleties. In another study, by ourselves and others, sensitive and non-sensitive persons were given perceptual tasks that were already known to be difficult (require more brain activation or effort) depending on the culture a person is from.
The non-sensitive persons showed the usual difficulty, but the highly sensitive subjects’ brains apparently did not have this difficulty, regardless of their culture. It was as if they found it natural to look beyond their cultural expectations to how things “really are.” 
Notice how depth of processing and noticing subtleties are related. All of the characteristics of being sensitive are related and interdependent.
The Value In Depth Of Processing
Depth of processing is an important gift of being a sensitive person. When HSPs take in information they take in everything which, although it can be overwhelming, puts the sensitive person in contact with more part of the web of nature and of life. It is a gift that supports the capacity of sensitive people to be seers and visionaries.
Unfortunately it can be hard to feel like you are not drowning in information. Sensitive people not only try to process all they take in but they also try to link information to a bigger picture as a way to develop a coherent understanding of the information they receive. It is a way to be conscientious and constructive at the same time.
Depth of processing is an important and valuable capability of sensitive people. It slows us down which is not always appreciated and understood but it is a part of being sensitive that is worth respecting.
 Author’s Note, 2012 for The Highly Sensitive Person, 9/6/2012, http://hsperson.com/pdf/Authors_note_HSPbk_Preface.pdf