Some people have a wrong idea about what evolution is, and they rightly think that their vision of evolution is nonsense and implausible. Monkeys don't change into people. And that's right, they don't. That isn't how it works.
For evolution to happen, you need three things.
1. When animals produce young, the young are a bit different from the parents.
2. The characteristics of the animal, are inheritable.
3. Something chooses which of the young will survive and reproduce, and which won't.
So, 1 is obvious. You are slightly different from your parents. Animals are diferent from their parents too, but since to us all sheep look the same, that isn't obvious. But it's true for all animals.
The differences might be, you're taller or shorter, you're more or less clever, your hair might be a different colour, your skin might be lighter or darker. You might be better or worse at seeing, hearing or smelling things.
We also know that characteristics are inheritable. "Doesn't he look like his father!" is something we often say, or "She's got her mother's nose". And if you look at dogs; two greyhounds make greyhound puppies, inheriting the characteristics of their parents. But if you mate a greyhound with a bulldog, you get something that is a bit like both, inheriting some of the characteristics of each parent. It's only relatively recently that we found out the reason for this, and we call the study of this "genetics".
Now consider dogs. For a very long time, humans have chosen which of the litter to keep, and which not to keep. As a result, there are numerous breeds of dog which are very different from each other. This demonstrates that it is possible, over a period of some millenia, that dogs can become many different breeds.
But dogs are still dogs. Greyhounds can mate with bulldogs (although I'm not sure how a chihuahua would cope with a Great Dane).
In this case, it was humans who did the choosing.
Another way for this to happen, would be for God to choose. If you believe in God.
The third way, is for nature to choose. If some of the lion cubs are faster, then they are more able to chase down prey; the slower ones will find it more difficult to catch prey, and will eat less well. The faster cubs are more likely to grow to adults and breed, and be able to feed their young. So pressure from their environment, pushes lions towards being able to run faster, or hide better, or kill more easily.
It takes generations. Evolution is slow. Animals don't change, it's populations that change, and they change in response to environmental pressures. But in a few short generations, we can already see changes; there are (and always have been) elephants without tusks. That used to be a disadvantage; tusks are useful tools. But today, a fine pair of tusks can get you killed for ivory. Tuskless elephants don't get killed for their ivory, because they don't have any, so are more likely to survive and reproduce. And they pass on the inheritable characteristic of "having no tusks". As a result, the percentage of tuskless female elephants has increased from 10% in 1969, to 38% in 1989. So here, although humans aren't intending to create tuskless elephants, human predation is giving that effect.
Natural evolution is even slower. The variations are quite small, and the advantage gained can also be small. But even a small advantage, over millions of years, can result in big changes.
For example, consider a populations of rabbits. Rabbits all over the place! And then, something happens, such as when the UK changed from being part of the continent, to being an island. Now there are two populations of rabbits, unable to interbreed because rabbits can't swim that far.
So what happens if the environmental pressures on the rabbits are different. Suppose the mainland rabbits are mostly predated by wolves; the island rabbits by eagles. On the mainland, natural selection will favour rabbits that spot wolves and get into their burrows quickly. On the island, natural selection will favour rabbits that spot eagles when they start to dive.
Mainland rabbits will be looking around them and listening for wolves; island rabbits will be looking upwards. On the island, selection will favour rabbits that mostly look up, and keep their heads turned up; also, they need better eyes, to see the eagle while it's still high up. Mainland rabbits will be favoured if they can run faster.
Over a long period of time, the island rabbits will tend to rest in a position that scans the sky and have good eyesight; mainland rabbits will develop more powerful running legs. Eventually, both populations will have changed so much (remember how much dogs have changed in only a few millenia?) that you wouldn't call either population rabbits any more. The island creatures are we now call skyscanners, and the mainland creatures are called fastrunners. And if you try to mate a skyscanner with a fastrunner, they are so different that they can't breed together.
And that's how evolution works.