Punnett Square
A Punnett square is a grid used to predict the possible genotypes and phenotypes of offspring from the alleles of two parents.
Definition
A Punnett square is a grid that shows all the ways two parents' alleles can combine in their offspring, with one parent's alleles listed across the top and the other's down the side so each box shows one possible combination; for a cross between two heterozygotes it predicts a $1:2:1$ genotype ratio and, with complete dominance, a $3:1$ phenotype ratio. It is really a tabular application of the product rule of probability: the chance of a given offspring genotype equals the product of the independent probabilities of the two gametes that form it, and phenotype probabilities follow from summing genotypes that share a phenotype, assuming Mendelian segregation, independent assortment of unlinked loci, random fertilization, and equal viability of every genotype. For $n$ heterozygous unlinked loci the square needs $4^n$ cells, so beyond two loci it is usually faster to compute each locus's probability separately and multiply them (the forked-line method).
Example
Crossing a heterozygous tall pea plant ($Tt$) with a short one ($tt$) fills the boxes $Tt$, $Tt$, $tt$, $tt$, predicting offspring about $50$ percent tall and $50$ percent short, while a dihybrid cross ($RrYy \times RrYy$) needs a $16$-box square to yield the $9:3:3:1$ ratio. For a trihybrid cross $AaBbCc \times AaBbCc$, the probability of all three dominant phenotypes is $(3/4)^3 = 27/64$ and of being homozygous recessive at all three loci is $(1/4)^3 = 1/64$, results a $64$-cell square would confirm, and observed counts are compared to such predictions with a chi-square test.
Key Insight
A Punnett square shows chances, not certainties, so a $1$ in $4$ chance of a recessive trait does not guarantee exactly one of four children will show it; with $100$ offspring, about $25$ showing the trait is expected, but $22$ or $29$ would not be surprising. The square works because meiosis is essentially a fair coin toss for each allele pair, and when observed ratios depart from its predictions, that departure itself points to linkage, lethal alleles, or non-random mating.