Self-incompatibility is like a rule in a game that says certain pieces can't fit together. For example, you might have a puzzle that has two different shapes, like a square and a triangle. The square piece can only fit into a spot that is shaped like a square, and the triangle piece can only fit into a spot that is shaped like a triangle.
In plants, self-incompatibility means that some plants can't breed with themselves or even with other plants of the same kind. Just like the square and triangle pieces in the puzzle, the plant has specific "rules" that determine which other plants it can mate with.
This happens because many plants have a special system built into their flowers that helps to prevent self-fertilization. The reproductive parts of the flower, like the stigma and the pollen, have certain molecules on their surface that can recognize each other. If the molecules are too similar, they will not allow the pollen to fertilize the flower, which means that the plant cannot reproduce with itself or with other plants that are too similar genetically.
This is important because if plants could breed with themselves or with other very similar plants, it could lead to inbreeding, which is not good for the health and diversity of the plant population. Self-incompatibility helps to ensure that new plants are created from a wide variety of genetic backgrounds, which helps to keep the population strong and healthy.