Here I will explain what evolution means by introducing some relevant terms step by step, and why it is a plausible explanation for how the life forms on earth become the way they are today.
There are lots of
SELF REPLICATING life forms on earth: plants drop seeds which grow into copies of that plant, animals breed and have babies which grow up to have their own babies. You should notice that they often have many similarities between them, for example a lot of animals have 2 arms, 2 legs.. notice that some animals look more similar to others. (e.g. monkeys and apes are similar, cats and dogs are similar.. but the distance between a monkey and a cat is bigger)
It has been found that these life forms all have a
DNA CODE, which is a special molecule that contains the script for how to create new copies of itself from scratch. The DNA codes have been found to overlap in similar looking creatures, every creature on earth shares some basic DNA codes but more complex creatures like humans have some of the longest DNA codes. People have been able to relate specific parts of the DNA codes with specific features - for example things like hair color, skin color, in humans and things like the breed of a dog can be found just by looking at its DNA. This DNA code can be changed and the changes are reflected in the life forms being different (e.g. someone took part of a jellyfish DNA code and put that into a pig, and they got a glowing a pig).
Two animals are said to be of the same
SPECIES if they can potentially breed with each other and create offspring that is also capable of breeding. Like how people have different colors of hair.. not every creature in one species is exactly the same. Imagine a species where only a fraction of its population has been born with an extra layer of fat around its body, and suddenly the climate dropped a lot so it's really cold and many of them die.. in this situation the few whose genetic code contained the instruction for keeping extra warm will die off less quickly and will have babies more likely to survive: After a few generations the majority of the species will have the extra layer of fat, this is called
NATURAL SELECTION. In fact there might be two different ways the can species survive.. in that case the species may split into two and perhaps eventually not be able to breed with each other.
EVOLUTION is the summary of these concepts: The self replicating forms which are best at surviving and breeding in their given environment will become prolific and by natural selection the mutations of their genetic code will be driven towards those which aid it. Some of the statements (such as existence of the DNA molecule, the scientific experiments I described, etc..) I made in previous paragraphs need to be backed up by evidence (and you will easily be able to find out about the evidence for it on the internet) but the logical of evolution is self evident in the sense that you can understand it and realise its truth by yourself (and as a testament to that, you can write a working computer program based on this idea).
A secondary topic, which is not as clear cut is how life on earth came to exist at all (because evolution clearly only explains how species can become mutated and developed into more species - not how some species of life came to exist in the first place). One plausible theory is called
ABIOGENESIS and it proposes that primitive DNA-like molecules were trapped in bubbles that were formed in chemical reactions near lava on earth many years ago. Just came across this relevant link
http://www.technologyreview.com/blog/arxiv/27827/