You want evolution explained in simple words? Okay.
If you have a population of animals, each individual will be slightly different. No two individuals will be exactly the same. Sometimes, these differences help the individual animal a little, and sometimes, the differences are a slight disadvantage.
If an individual has a difference that gives it a slight advantage, then this individual will be better able to withstand some pressure it is put under. It could be an advantage that gives it slightly more stamina, so it is more likely to escape when a predator attacks. Maybe it is better able to deal with droughts. But it will be more likely to survive long enough to produce offspring. Since the differences are caused by genes, and since genes are passed from parent to offspring, there's a good chance that the offspring will get the same genes that helped the parent. And so the offspring that get these genes will have the same advantage.
If the individual has a difference that hinders it - maybe it has slightly poorer eye sight, or it has a deficiency in its immune system - then this disadvantage is going to mean that the individual is more likely to die from this weakness than an individual that does not have that weakness. As such, it has a reduced chance of living long enough to reproduce. Since it is less likely that this disadvantaged individual is going to reproduce, it means that it is less likely that the genes that caused the disadvantage are going to be passed on.
So, the genes that help an animal survive the pressures it faces are going to have a better chance of being passed on and any genes that reduce an individual's ability to survive are less likely to be passed on. As a result, the genes that cause individuals to be better adapted to their environment will gradually spread throughout the population over many generations. A change that was once present in just one individual will end up being in ALL individuals.
When many such small changes occur, we will see the population evolving over many generations to have new adaptations that help them, will losing traits that do not help them.
If you think any part of that is wrong, please tell me which part.