Evolutionism is a scientific theory. What it means is that it's well documented and well explained. Cows turning into whales it's not the way it works. The explanation is way more complex than that, but while it is complicated, it does explain how animals evolve, that's the point of the hole fucking theory...
Since you've challenged someone to explain it, I'll try to do it for you:
The theory of evolution was born with Charles Darwin, an english scientist that proposed a radical new explanation for the origin of lifeforms we have today. Opposed to the mainstream scientific community of the time, that was fixist and believed that every lifeform we have exist in a form that doesn't change at all, he proposed the idea that species mutated over time, and that you can find relations between species.
So how does it work? Every lifeform has a thing called genetic code, a dna. For every individual you have a genome that is unique. It's a very complex sequence of, let's call it information, that will determine if you are a man or a woman, if you are tall or not, the colour of your skin, etc... Every individual, thus is unique.
So, as said before, every individual has a different genome. But there's a lot of lifeforms that have very close genomes, so close in fact that the differences are minimal. You can reproduce with these lifeforms, and your progeniture can reproduce as well. That is the definition of a species. If you can't reproduce with a monkey, then most certainly a monkey and a man are a different species, that's pretty straightforward right?
Ok, let's continue. This genome is as said before very complex, when you reproduce with another individual, you will give a part of your code to your progeniture, and your mate will give a part of his own. However, the human body isn't perfect, and there's a series of "copy-paste" errors that are made when you reproduce (it also happens in a certain % when cellules duplicate as well). Differences in your genetic code that are called mutations. Most of the time they don't do anything, but sometimes they make you different.
These differences may be bad for your survival rate in nature (genetic diseases for example) or good for it (longer legs that let you run faster). By natural selection, individuals with poor mutations die, and with good mutations survive. That make them slightly different then other individuals.
Over time, successive progenitures will cumulate these genetic differences, and if these individuals don't reproduce with other individuals with their own unique set of mutations, over time their genetic differences will increase. At some point, they are so different, that they cannot reproduce anymore, and thus they are different species. That's how evolution works.
The theory of how life evolves is then the one of these successive mutations over millions of years that transform life. If you move up your genetic tree, at some point it will cross my ancesters. And if we continue going up, we will reach the first couple of our kind, homo sapiens (funny enough, scientists call them genetic Adam and Eve lol).
The ancesters of these first homo sapiens were different, if you keep going up you can reach what we call our first common ancester with another species. These common ancester gave birth to individuals that would then by reproduction create progenitures that were further and further genetically appart, creating the homo sapiens "branch" of the family in one side, and let's say the homo neandertalis "branch" in the other.
If you keep going up, you will be able to find a common ancester with chimps, then with all primates, keep going up and you will find a common ancester with all mammals, etc...
It's not that a cow can evolve to a whale. Although that'd be awesome, it's not really possible. What exists is that at some very distant point (millions of years) whales and cows had a common ancester, and it's kids just evolved differently.
That's how the evolution theory works. Now, you probably want some hard evidence. Well, I'll give you a few examples that corroborate evolution:
- Diseases evolve, all the time. When you are confronted with a disease, your body creates anticorps that kill it, and if you get the same disease again you will be more protected against it (btw that's more or less how vaccines work). Well, viruses and bacteria reproduce a lot, and very fast, which offers them the chance to mutate a lot, these mutated diseases will have protections against your anticorps, and are allowed to survive and reproduce through evolution. The HIV virus for example is a master of adaptation, it's impossible today to kill him. That's because it evolves so fast that your body can't keep pace with his evolutions, and even our best medicine can't do anything but reduce his strenght. It's a so powerful virus that he's actually capable of killing your defensive system, thus killing you as well.
- Dogs. Dogs are one primary example of evolution, you can breed them to create pure-races, you can alterate your progeniture by choosing how to reproduce them. If you breed two dogs, take the smaller dogs, make them breed, then take the smaller dogs and make them breed, ... in a couple of generations you will have very small dogs, different from the ones you had in the first place that's a forced evolution made by man. It's believed that dogs were very similar to wolves up to tens of thousands of years ago, when humans started to domesticate them, and to breed them into the loyal companions they needed to survive (btw, when two species cooperate to increase survival odds, that's called coevolution).
- Gallapagos Finches. These were birds Darwin found in Gallapagos. There's many kinds of finches: large ground finches, medium ground finches, small ground finches. Then there's several types of seeds they can feed on: small seeds, medium seeds, large seeds. Large grounds are good to eat big and not as well for medium sized seeds while small aren't possible, small grounds are good for small and at large for medium ones, while medium grounds work well for medium seeds, and a bit for big and small seeds. Now let's say humans like to use the wood of the trees with medium seeds and small seeds to make their benches, but they really don't care about the wood of big seed tree. He just start chopping the trees he needs and leave the trees he doesn't need. When he finished almost all trees of the forest, he leaves in his boat to go home. A few years later scientists come back to the island, they realize that now there's almost only big ground finches, a few medium ground, and no small grounds at all, while the population was better shared before. In a kind of natural selection, the types of finches more fit to survival, managed to stay alive and reproduce. In the place of 10k LG finches, 10k MG and 10k SG, now you have 25k large ground finches, 5k MG finches and almost none SG, as the trees with big seeds are now the only ones in the island and took the place of the other trees. You can assume that the mutation with big grounds will be able to keep eating, and reproducing, they survived because of their mutation. A while later, conditions restabilize with diverse seed sizes of trees, but now only the progeniture of these LG finches exist in the island. Finches of another island arrive with a migration, but they lived in another island and evolved differently, they can't reproduce anymore with this other group of finches descendents, which has become a totally different species because of evolution.