CUDA is a nvidia technology that allows to employ the graphics card for general computations. For specific, high-dimensional problems modern GPUs are significantly faster than usual CPUs which makes this CUDA highly interesting, especially for scientists relying on numerical simulations.

I'm using the thrust library as a convenient way to port numerical algorithms on the GPU without digging too deep into CUDA details. Thrust provides CUDA ports for the C++ STL algorithms and makes GPU programming really easy. For a short introduction have a look on the slides of my talk about thrust: