Dissipation

In physics, dissipation includes the concept of a dynamical system where "important mechanical modes", such as waves or oscillations, lose energy over time, typically due to the action of friction or turbulence. The lost energy is converted into heat, raising the temperature of the system. Such systems are called dissipative systems. 
For example, a wave that loses amplitude is said to dissipate. The dissipative nature depends on the nature of the wave: an atmospheric wave, for instance, may dissipate close to the surface due to friction with the land mass, and at higher levels due to radiative cooling.
In computational physics.
In computational physics, a numerical dissipation is also known as "artificial dissipation" or "artificial diffusion" or "numerical diffusion". They all mean this: when the pure advection equation--which, by definition, "is free of dissipation"--is solved by a numerical approximation method that reduces the amplitude and changes the shape of the initial wave in a way analogous (similar) to a diffusional process, the method is said to contain 'dissipation'.
In river hydrology.
In Hydrology, dissipation is the process of converting mechanical energy of downward flowing water into thermal and acoustical energy. Various devices are designed in stream-beds (river-banks) to reduce the kinetic energy of flowing waters to reduce their erosive potential on banks and river bottoms. Very often these devices look like small waterfalls or cascades, where water flows vertically or over riprap to lose some of its kinetic force.