Neuroscience refers to the study of human brain and its function: it represents the "medical" side- it focuses on the biology and chemistry of the brain.
Cognitive Neuroscience ties the biochemistry of the brain to its cognitive functions.
Basically, Cognitive neuroscience helps us understand than many cognitive functions have a biochemical reason, for example anxiety, and can be cured by medicine - it shows us we possibly have less control over our brains than we think (or more, if we use this knowledge, but less by for example thinking positively)
