Environmental pressure is another term for natural selection, a process that encourages some genes to survive because they are conducive to the environment while others die. This process slowly causes a distinct species to evolve over time.
Environment is an important factor in how species evolve. In many cases, genes that have survived time and time again are adaptable to climatic and environmental change. For example, humans evolved to upright movement because walking upright was more conducive to surviving in a variety of environments. Genes that featured this upright movement were passed on from parents to children through natural selection. A similar process caused the evolution of hand dexterity, starting with the ability to make tools out of stones and wield those tools.
As another example, horses that could feed on both grass and leaves replaced those ancestors that only fed on grass because the former could survive on a variety of food when grass was scarce. They were best suited to survive.
Part of natural selection is biological fitness. Natural selection and evolution don't work unless an organism can live long enough to reproduce, the definition of biological fitness. Reproduction creates organisms that have a variety of traits, either as gene mutations or gene combinations from two different parents. At the same time, more organisms are born then can survive, making it necessary that those most fit to survive with the most effective gene combinations do so. Meanwhile, the weakest do not survive, failing to pass on their genes.