Malthus argued that the human population was increasing at an exponential rate, and that under the best of conditions, food supplies would only increase linearly. Thus, he said that at some point, the population would become greater than the amount of food available to support it. So, there would be massive competition for the very limited resource of food.
Darwin extended this basic idea to say that all organisms are always competing for limited resources, and that any change which benefits an individual would be passed on to its descendents making them more fit and better able to survive and reproduce.