Kinetics (as used by chemists) refers to the study of rates of chemical reaction. This is very important as in
organic chemistry you can often get several different
products from the same mixture of
reagents, but by controlling the reaction conditions the rate of formation of each product may be changed. Knowledge of the kinetics of a reaction helps to produce larger quantities of desired products while reducing the presence of unwanted byproducts.
Getting back to the point, rates of reaction are generally determined by two types of variable: temperature, and the concentration of each reagent.
You can see how this dependence works for a simple reaction if you think about it just a little. A group of molecules can only react if they are all together and if they have energy to form an activated state. Dealing with bulk quantities of materials, you need the probabilities that each type of molecule is in the same place and the probability that enough energy is available. The amount of energy is related to the temperature by a function familiar to anyone who has ever used thermodynamics or statistical mechanics. The probablility of a molecule being in a given place can be measured by the concentration of the molecule.
Needless to say, if you need N molecules of substance A in the same place, the probability of that happening is proportional to the concentration of A raised to the Nth power. The reaction is said to be Nth order with respect to A.
This also gives a 1st order differential equation which allows you to predict the rate of reaction for a simple reaction, but often reactions are more complex. Often you have intermediates, which act as products in one step of the reaction and reagents in the next step. This gives you a set of differential equations which must be solved simultaneously. This set of equations can always be reduced to a single differential equation of higher order, but may be nonlinear if the same reagent is involved in multiple steps of the reaction.
To make things more complicated, you usually don't really know the concentrations of the intermediates, and often don't have any way of measuring them. This is where the steady state approximation is useful.
Basically, for the steady state approximation you pretend the concentrations of the intermediates is constant over the entire duration of the reaction, even if you don't know what it is. Looking at the set of first order equations, you take each equation where a given intermediate is produced or consumed to get an equation describing the concentration of that particular intermediate in terms of concentrations of reagents, products, and other intermediates. Then you go back and substitute that equation for the intermediate concentration in the original equations, and repeat the process with another intermediate, until all you have left are concentrations of product and reagents.