Evolution describes the development of useful genetic traits in species of organisms through the natural pressure to survive in specific environments. Life forms that develop traits that don't help them survive die out. The ones that develop traits that sustain or improve their chances of survival until they can produce viable offspring continue on. Every organism comes from a long line of predecessors who were lucky enough to successfully cope with their environment as it changed over time.
The Big Bang could not have produced life itself. Conditions simply did not permit it. But the expansion of matter and energy from a condensed, indeterminate state out into time and space eventually made it possible for distinct forms of matter and energy to form. From those elementary particles and forces, atoms naturally formed and reacted with each other in predictable ways. These are the types of reactions that chemicals do even today.
It was only after a great deal of time that enough reactions had occurred that chemicals complex enough to support energy transfer and conversion developed. This was not what we would call life, but the processes were the ones that life forms control and use. At some point, a molecule made a copy of itself out of simpler materials, and this might be considered the beginning of life. For this to happen, information had to be chemically stored to make the copy possible. We call this storage system a gene. From that point, every step of evolution has been a matter of slight, natural changes in genes proving to be either beneficial or deleterious for continued survival and reproduction in an environment. Successful organisms often tended to be more complex and adaptable to change, so that environmental shifts had less of a catastrophic effect. Other organisms stayed simple and survived simply by being impervious to change or finding environmental niches where change seldom occured.
As life became more complex, it reacted with its environment on higher and higher levels, first groping its way around and finding nutrients by accident, then learning to recognize and follow light, sound or scent. At some point, some life forms became "aware" of their environments, learning to recognize repetitive situations that were beneficial (food, mates) or hazardous (predators, hazards) to their continuation. Thier ability to pursue/avoid significant parts of their environment were instinctive, but controlled by a nervous system genetically trained to manage it.
Further development enabled organisms to share information with each other, communicating, teaching and learning so that all the survival information didn't have to be packed into genes. Ultimately, developing organic brains managed the trick of combining awareness, memory and abstract thought, the ability to think about things as ideas, not just objects. This enabled the brain to plan for situations that had not yet occurred, develop tools to prepare for future situations, and even to think about itself. With self-awareness and abstract thought, the first primitive humans had developed, able not only to cope with their environment, but to control it to some extent.
Each step in evolution amounted to nothing more than a successful adaptation, a trait that made survival or reproduction easier. There was no conscious effort to direct change, only the natural selection of survival or extinction. If you lived, you likely had children to inherit your genes. And at the most basic level, every mechanism involved in living is simple, predictable chemistry, unrecognizable at the macro level, as we perceive "life".