The reaction rate is nothing but a measure of how fast or slow a reaction proceeds. That is, how quickly do we get the products from a certain reaction. It is given as the rate of change of the concentration of either the reactants or the products. Mathematically, the rate of a reaction is given as:
dC/dt = k*C^n
In this equation dC/dt is the rate of the reaction. C is the change in the concentration of chemical reactants or products and t is the change in time. k is the reaction rate constant and n is the order of the reaction. Remember, in a reaction, reactant concentration decreases as the concentration of products increase. Hence, if we talk about the rate of reaction using reactant concentration, rate will be negative and for products, it will be positive. Also, reactions can be of 0 order, first order, etc. Rate of reaction is a function of temperature and in general, for every 10 degree Celsius increase in temperature, the rate of the reaction doubles.
Hope this helps.