CFD is the systematic application of computing systems and computational solution techniques to mathematical models formulated to describe and simulate fluid dynamic phenomena.

CFD is part of computational mechanics, which in turn is part of simulation techniques. Simulation is used by engineers and physicists to forecast or reconstruct the behaviour of an engineering product or physical situation under assumed or measured boundary conditions (geometry, initial states, loads, etc.). A variety of reasons can be cited for the increased importance simulation techniques have achieved in recent years:

Need to forecast performance
Cost and/or impossibility of experiments
The desire for increased insight
Advances in computer speed and memory (1:10 every 5 years)
Advances in solution algorithms
The simulation of flows is accomplished by:

Solving numerically partial differential equations (PDEs),
Following the interaction of a large numbers of particles, or
A combination of both.
CFD, by its very nature, encompasses a variety of disciplines, which may be enumerated in the following order of importance:

Engineering
Physics
Mathematics (classic and numerical analysis, discrete mathematics)
Computer Science (algorithms, coding, software)
Visualization Techniques
User Community (benchmarking, documentation, teaching)