CUDA Cores -- Just a small part of the larger whole when it comes to an nVidia GPU. A "CUDA Core" is nVidia's equivalent to AMD's "Stream Processors." NVidia's proprietary parallel computing programming model, CUDA (Compute Unified Device Architecture), is a specialized programming language that can leverage the GPU in specific ways to perform tasks with greater performance. Each GPU can contain hundreds to thousands of CUDA cores. Architecture changes in a fashion that makes cross-generation comparisons often non-linear, but generally speaking (within a generation), more CUDA cores will equate more raw compute power from the GPU. The Kepler to Maxwell architecture jump saw nearly a 40% efficiency gain in CUDA core processing ability, illustrating the difficulty of linearly drawing comparisons without proper benchmarks.
CUDA Cores are parallel processors, just like your CPU might be a dual- or quad-core device, nVidia GPUs host several hundred or thousand cores. The cores are responsible for processing all the data that is fed into and out of the GPU, performing game graphics calculations that are resolved visually to the end-user. An example of something a CUDA core might do would include rendering scenery in-game, drawing character models, or resolving complex lighting and shading within an environment.