When I was growing up the general idea of what people define as "evolution" now was simply "adaptation" then. A creature's ability to be flexible & to change and grow based on its environment so that it does not die out -which makes sense.
There are two kinds of adaptation. One is based on genetics but is not genetically inherited. An example is muscle mass - the more you use your muscles the bigger they get. That is not inherited (i.e. if you work out a lot your daughter isn't born with bigger muscles.)
The second sort IS inherited. If you are born with the genes to be slightly taller, and because of that you survive while others who are shorter die, then your children will likely be taller. In the short term this is often called adaptation; in the long run this is evolution.
Let's take a simple example - whale evolution.
Pakicetus was a land animal about the size of a wolf. He had canine-like teeth, nostrils in the front, four legs, a long tail and fur. He lived about 50 million years ago and spent most of his time on land. His eyes were high (like a crocodile's) and so he could also wade around in water while keeping his snout and eyes above the water. This let him catch a few fish as well.
The next step in whale's evolution was simple adaptation. Ambulocetus evolved from Pakicetus. He was very much the same - same body plan, same skeletal structure. However, since Pakicetus had a lot of luck sitting in the water eating fish, Ambulocetus had some adaptations that let him eat fish more effectively. He had flatter feet (better for swimming) and a stronger tail (for swimming.) He had lost his external ears, which is an adaptation that many aquatic animals have since ears don't work well underwater. His nostrils were a little higher to help him sit in water like a crocodile and wait for prey to swim by. However, he could still walk; he still had legs and hips with strong muscles and thick bones to resist gravity.
That's all just adaptation, right? Modification of existing structures.
The next step was Kutchicetus. This guy was a little smaller. His nostrils were higher. He could still lumber around on land, but not very well. His tail was getting stronger and thicker, and he was using it almost exclusively for swimming.
That's all just adaptation, right? Modification of existing structures.
After Kutchicetus came Rodhocetus, which still had legs but could no longer walk on land. (Think seals, which can wriggle onto the sand but can no longer walk.) He was starting to look like a whale - fat tail, small legs, nostrils moving upwards into what we would now call a blowhole. However he didn't have a lot of blubber yet and still relied on fur to keep himself warm.
Next came Dorudon, which lived about 40 million years ago. He looked a lot like Rodhocetus, but had very short rear limbs that were useless for swimming so he relied more on his tail. His pelvis had started to disappear since he didn't need it any more. He had started to develop blubber to replace fur since blubber is more effective underwater. This also allowed him to dive deeper. They could likely make clicking noises but if they could their echolocation abilities were pretty limited.
That's all just adaptation, right? Modification of existing structures.
Next came the Odonocetes. You probably know one of these pretty well - Tursiops truncatus, the bottle-nosed dolphin. He lost his rear legs completely, although some dolphins are still born with vestigial rear legs. He had a "melon" which was a structure on the top of his snout that focused sound waves. This wasn't new; it's just an adaptation of facial fat that all the above animals had.
Again, all just adaptation, right?
But over 50 million years those small adaptations can turn a "wolf" into a whale. (Or a dinosaur into a bird, or a mouse into a human, or a bacteria into a hydra, or a hydra into a flatworm, or a flatworm into a fish.) And that's what evolution is.