A cellular automaton is a discrete dynamical system, where states taken from a finite set of possible values are assigned to each site (or cell) of some regular lattice (usually Zd, for some dimension d). At each time step, the states of the cell and its neighbours are used by a function (the CA rule) to compute the new state of the cell; this is applied simultaneously to all cells, generating a new configuration.
Cellular automata are useful models for complex systems of many identical (and usually spatially fixed) elements when the dynamics depends only on local interactions.
Number conserving cellular automata (NCCA), or conservative cellular automata, represent a particular and interesting class of CA, in which the states are numbers, and the function has the special feature of preserving the sum of the states (over all the configuration, which is supposed to be either periodic or finite), when the states are updated.
An interesting feature of NCCA is that they can be seen as systems of indestructible particles, moving according to certain rules. The states are then interpreted as the number of particles occupying each cell at a given time. Since there is, in general, no inertial movement, no potentials, etc., it would be perhaps more appropriate to talk about simple "agents" instead of "particles".
This property arises naturally when modelling phenomena such as highway traffic, fluid flow, eutectic alloys, the exchange of goods between individuals, etc.; more generally, as "the modelization of the physical conservation law of mass or energy" (Imai). Moreover, number-conservation is an interesting property in itself: if it is recognized in a cellular automata, it may help to prove further dynamical properties. Finally, the class encloses a wide range of possible behaviors; in fact, any CA can be simulated by a NCCA.