It is simply less probable than only one out of four puppies having a genotype of mm. Since an individual has a pair of each chromosome, they have two copies of the gene. This simple case of a single gene is called a monohybrid cross - simply meaning that there is one gene and two possible alleles for that gene. It is quite rare for an aspect of an organism's appearance to be controled by genes as simple as this. Consider that each gene is a length of DNA with many base pairs - many possible sites where a mutation could produce a change.
All genes have the potential to come in lots of mutant flavors - lots of alleles.
It is simply a matter of figuring out the alleles in each parent, lining them up on the top and side of the square and filling in the boxes with one allele from each parent. In a dihybrid cross we consider Two independent genes. If we have two genes that are independent, either copy of each could end up in a reproductive cell with either copy of the other. Thus our Punnett Square needs to have four rows along the top, and four rows along the side - to consider all four possible combinations of the two copies of the two genes. It is rare that an aspect of an organism will be controled by a single gene that has just two alleles.