Genetics. You have to be pretty well-rested to get your head around it, and after last night's performance from my 18-month-old, well-rested I am not. I wonder if wakefulness is genetic? Here goes, anyway...
It is possible for two non-twin siblings to be identical, but very very unlikely. On average, we are 50% genetically similar to our siblings. Tell that to my two boys, who constantly get asked if they are twins!
Your commonplace human being has 23 pairs of chromosomes in nearly every cell of their body. One exception is in the man's sperm and in the woman's egg cells, where there are only half the number of chromosomes, one of each of the 23 pairs. To ensure that we don't end up all looking the same, when the pairs split in a sperm or egg cell, a process called recombination occurs, which is basically a scrambling of the DNA in each chromosome.
When a baby is made, the 23 chromosomes in the sperm and the 23 in the egg match up, making a unique human being, which has two copies of each of its unique genes.
So imagine the mother, with two copies of her own genes, meets with the father, who has two copies of his genes, then each trait they pass to their children is like the flip of a coin. Heads, you get stubbornness, tails you get double-jointedness, etc. It is very unlikely that you will get the exact same combination of heads and tails on 23 flips of the coin, two times over.
Make sense? Of course it doesn't, it's about the human body, a magical machine.
Mummy gave you this, daddy gave you that
If your child did ask this question, I guess the best way to explain it would be to say that you are half mummy and you are half daddy, but there are many different ways in which you can be like mummy and many different ways you can be like daddy. So each of your siblings is like mummy and like daddy in different ways.
Science fiends, please feel free to correct me in the comments!