This is a basic explanation that presents some common sense, everyday evidence supporting evolution to help you understand it. Evolution occurs in both positive and negative ways. For example, dwarfism almost being eradicated even though it is a dominate trait. Dwarfism is a “negative” evolutionary trait that was weeded out because taller humans were faster and stronger which enabled them to have a higher chance to live.
When you have a higher chance to live, it is more likely that you pass on your traits to the next generation and you have more kids which in turn have a better chance to live longer. Although, genetics is like a bell curve of probability. For example, I am taller than anyone in my family, this is unlikely because both of my parents were average height. My brother is also average height. I am a statistical outlier. But due to this, I have a higher probability of having a taller child than my brother. I may or may not have a taller child (which is why 99.999% of all species are extinct, not that I am suggesting I am my own species or anything, just an example) but the probability increases for a tall child like a basic bell curve in statistics (where you would start at 0, this depends on your partner too, but just a rough example). To the point where my great X30 grandchildren, if in the perfect circumstances, could all be 7 foot tall giants. My brother, if he has kids (low probability) that are like 5’2, they could become dwarfs in 500 years if this statistical unlikelihood occurs. This is statistically unlikely (for a few generations), but possible over millions of years.
The driver of evolution is natural selection. Natural selection is like a filter for water. Depending on the holes in the filter, different types of things get in. Some things actually make it through the filter that shouldn’t by chance, such as a stick that goes through perfectly perpendicular and slips through. This is seen in nature with albinism. Naturally, when something is albino, predators can more easily spot it in greenery and soil (sometimes it survives as a heterogeneous trait and sometimes the animal manages to have kids). BUT! If you change the filter holes, albinism could be good! such as Polar Bears at the north pole because of the snow! Polar bears/albino snakes probably occurred other places, but died due to the lack of camouflage. But, statistically speaking, that genetic variation has a small chance to slip through the cracks in a forest environment, which is evidenced by albinism still happening today.
Heterogeneous traits (recessive traits there but overruled by a dominant) such as this situation have a higher chance to stick around. But some die out. For example, if a heterogeneous albino lizard (doesn’t present white skin) mated and passed on his heterogeneous genes to only one child who is also heterogeneous, then the lizard dies, but the lizard’s child is then eaten before it reaches adulthood and doesn’t pass on its genes, therefore ending the bloodline. But the opposite can happen where a lizard has 20 kids and one presents albino and the other 19 go on to propagate the “tainted” gene and occasionally end up with another albino child but the gene remains.
These genetic variations happen EVERY DAY but they are so minute and rarely amount to anything everyone wants to deny it and say “well why don’t I sprout a third arm!!!” “Evolution” occurs by genetics variation and mutation in the process of making a child over a long period of time. From “positive” evolution like making me taller at birth, and therefore more attractive (statistically desirable) to more women which gives me a better chance to pass on my genes which have a statistically good chance to be as tall/taller than I am and their kids and so on. To “negative” evolution, such as down syndrome, which makes you significantly less likely to have kids or to be able to survive in the wild (humans don’t really have significant natural selection).
Want concrete current evolution evidence? Look at Mules and Ligers. They are completely different animals and have far greater characteristics than their parents. BUT! They can’t dominate because they are sterile and can’t pass on their genes.