Vile Atheist
Loud and Obnoxious
I'll try to be as simple as I possibly can.
Obviously, you and I are different and we're different because we have different genetics. We're still of the same species, but there are genetic differences between us that make you you and me me. Indeed, these genetic differences exist in all life (with some exceptions that will just needlessly complicate things further if I explain it at this point).
When two "parents" reproduce, they may do so imperfectly (in the case of asexual organisms, there's only one "parent", of course). What I mean by that is during reproduction, DNA needs to get copied and it's sometimes copied incorrectly. The body naturally tries to repair such genetic damage. Sometimes it is successful, sometimes it isn't. If it isn't, that leads to a mutation. Sometimes the mutations lead to a beneficial outcome, sometimes harmful, sometimes neutral.
The result is that sometimes traits develop that may be slightly more useful to an organism or sometimes it may have negative consequences. The ones affected by the negative consequences tend to die off because they either can't compete for resources or mates or evade predators or what have you. The ones that have positive mutations tend to reproduce more because they have an advantage and those genes get passed onto the next generation. This is basically natural selection.
Natural selection takes its course on a population. The members of a population with "bad" mutations die off easier and their "bad" genes don't tend to get passed on. The ones with "good" genes tend to reproduce better and their genes tend to get passed on. By "good and bad", I mean this in the context of "better suited to their environment".
Eventually, what may happen over time is that a population will get separated from another by some geographical barrier (being on an island, across a mountain range, or even just a large distance). As a result, there are different selection pressures on the two groups. Over time, with the two groups undergoing different selection pressures (nature demands different traits to be better suited to the environment), the two may become so genetically different that they can no longer breed with each other, or at least not form viable offspring. This is called allopatric speciation. There are other types of speciation too (other means by which species can form, but this is the easiest to visualize).
It's tempting to think of evolution as being geared towards evolving human-like qualities because it's obvious human-like qualities are to our advantage. But think of an antelope on an African grassland. Its existence depends on being able to evade larger predators like lions. It can do this through several ways like being able to detect lions better to give them more reaction time. This is why an antelope's eyes are further to the sides of its head. It gives it a better field of vision. It's why an antelope's ears stick up and out. It gives it better hearing. This is why antelopes have long, slender legs. It allows the antelope to run faster. It is evolutionarily advantageous for an antelope to develop consistently better eyesight, hearing, camouflage, and speed to avoid being hunted.
Meanwhile, the lion that's trying to hunt it needs better ways of catching an antelope. The selection pressures would favour lions that have sharper teeth, sharper claws, more powerful legs so it can run and jump faster, etc. The result is a sort of "arms race" between the predator and prey. The predator wants to catch its prey, so it tends to evolve traits through natural selection that favour catching the prey. The prey doesn't want to end up as lunch, so it tends to evolve traits through natural selection that favour evading the predator.
I hope that explains the basic concept to you.
