Definition
Mendel's laws of inheritance are the basic rules of genetics that explain how a parent's biological features (traits) are passed on to its offspring. People used to think parents' traits blended together like paint. Mendel showed that genetic information is passed on in separate, unmixed units, like individual grains.
You inherit bricks, not paint
Mix red paint and white paint and you get pink. You can never get the original red or white back. Long ago, people believed heredity worked the same way: a parent's traits got mixed together like paint and handed down to the child.
But Gregor Mendel, an Austrian monk, grew pea plants and found something very different. He crossed round peas with wrinkled peas. In the first generation of offspring, strangely, every pea came out round. The wrinkled trait seemed to have vanished completely.
Then he crossed those offspring with each other. Surprisingly, the wrinkled peas came back in the next generation, and round and wrinkled peas appeared in a ratio of about 3 to 1. The wrinkled trait had not disappeared. The information for it was hiding out of sight. We call the trait that shows on the outside dominant, and the hidden trait recessive. Genetic factors come in pairs, and they separate when reproductive cells are made. This is the law of segregation.
Traits roll like separate dice
Imagine flipping a coin in your left hand and rolling a die in your right hand at the same time. The coin landing on heads has no effect on whether the die shows a 6. The two results are completely independent.
Mendel looked at what happens when two different features of a pea are inherited together: its shape (round or wrinkled) and its color (yellow or green). It turned out that whether a pea was round or wrinkled made no difference. The color followed its own rule and split into yellow and green independently.
So two or more different traits are passed on independently of each other. This is called the law of independent assortment. Because the many traits you inherit from your parents combine independently, like separate dice, brothers and sisters from the same parents can still end up with very different faces, heights, and body types.
To be a bit more precise
To be a bit more precise, Mendel's laws do not fully explain every kind of inheritance in nature. The seven pea traits Mendel studied happened to follow a very simple, tidy pattern in which they don't interfere with each other.
In real organisms, there is incomplete dominance, where a red flower and a white flower produce a pink one. There is also polygenic inheritance, where a great many genes work together in complicated ways, as with human height or skin color. And there is linkage: two genes sit side by side on the same chromosome, so they don't split apart like separate dice and are inherited together as a bundle.
Still, the real greatness of Mendel's discovery is that he was the first to see the core idea: genetic information is passed on in grains that do not disappear. A parent's genes are not a liquid that gets mixed and watered down. They were clear code blocks that can skip a generation and come back whole at any time.
Common misconceptions
A dominant trait is better and stronger than a recessive trait.
'Dominant' and 'recessive' only describe which trait shows up first on the outside when both genes are present (which one is expressed more strongly). They carry no value judgment at all. A dominant trait is not biologically superior or more advantageous.
Where you meet it
When you cross a round pea with a wrinkled pea, only round peas show up in the first generation of offspring.
Even when both parents have blood type A, each can carry a hidden type O gene. If those two genes meet, a child with type O can be born.
In one sentence
A parent's genes don't blend and vanish like paint. They stay as separate units, like LEGO bricks, and are passed on to the next generation.