Charles Darwin is known as the 'Father of Evolution' for his theory of natural selection, which is now almost universally accepted, but which was deeply controversial when it was first proposed.
Maybe that's obvious to you, or you've learnt about it at school. But in case it's not, I'll give you an example.
Say a bird lays some eggs, and when they hatch, one of the baby birds happens to be much better at flying than all the other babies - in fact, better at flying than this type of bird ever usually is.
When this baby bird grows up, she will probably be better than her brothers and sisters at escaping from cats or hawks, or whatever else wants to eat her. That means she will live longer, which means she will lay more eggs and produce more babies of her own than her siblings. Some of her babies will also inherit her flying ability. So, from one super-flying bird, we now have several. And all of these super-flying babies will grow up into more successful adults than their wonky-flying brothers, sisters, and cousins, breed more than the less good flyers, and pass on this skill through their genes to some of their own offspring. After this has happened quite a lot of times, this species of bird will fly better than it used to. This is called evolution - the change from something into something else - by natural selection.
Charles Darwin, photographed by Julia Margaret Cameron in 1868. Presumably, he didn't always have such a grizzly beard.
Natural selection is the process by which a more successful variant of a species breeds more offspring.
One of the interesting things about natural selection is that it applies to all kinds of characteristics. Sticking with birds for a moment, you could have a different bird who sings better than his brothers and sisters. His beautiful singing might attract more females, so he will get more chances to breed. There will be more eggs with his genes in them, and again, he will pass on his genes to some of his offspring. Among his babies, the operatic offspring will be more successful than the ones that don't sing so beautifully. Gradually, there will be more and more birds that sing beautifully.
HOWEVER, natural selection works both ways, and how well a particular variation works - how successful the different baby is - depends on where and how it lives. Say that the same bird with the beautiful voice lives in a place where there are owls who hunt using sound to help them find their prey. His singing will attract the hunters' attention, and he's likely to get eaten much sooner than his quieter brothers and sisters because one of the owls will hear him. That means he won't breed as much - maybe not at all if he starts out singing in the nest before he has fledged - and any babies he does have who inherit his beautiful voice will also get eaten more quickly than their brothers and sisters. After a few generations of that happening, you won't find any birds with beautiful voices where there are owls who hunt by sound.
So what natural selection does is to favour those differences that crop up randomly and help the individual to survive better in their environment. Another example: it might be good for a monkey to be able to eat some red berries that make all the other monkeys sick, because there might come a year when all other kinds of food are scarce. When that happens, the only monkeys that don't die of starvation will be the ones descended from the first monkey that could eat the red berries. Eventually this kind of monkey will evolve to eat those berries. But if these monkeys specialise too much, and start only eating the red berries and nothing else, then in a year where the red berry bushes die from drought, the specialist red berry monkeys will starve, and the only ones that survive will be the ones that eat lots of things including the berries.
This might all sound logical and obvious to you, but before Darwin's time, it wasn't. Moreover, when he published his theory in 1859 in a book called On the Origin of Species, the fact that he said that the theory of evolution by natural selection applied to humans in just the same way as to animals and plants - which meant that humans and apes had evolved from a common ancestor - horrified and outraged quite a lot of people. Most people at that time were Christian believers, and they saw Darwin's theory as contradicting a lot of what was in the Bible, not least God's creation of Adam and Eve. It took over ten years before people really began to accept the theory, and even today, there are still creationists who believe God literally created the world in seven days, and who continue to reject Darwin's theory, despite mountains of evidence for it.