In the first column, both parents are homozygous wild. In this case the child is guaranteed to be homozygous wild, also, because both parents will contribute a 0 at this locus. By similar reasoning the fourth locus in the child will be homozygous mutant, since both parents are forced to contribute a 1.
In the second column one parent is heterozygous at this locus, and there is an even chance of passing a 1 or a 0 to the child. The second parent is homozygous wild, and will always contribute a 0. Thus the child will either be 10 or 00.
The third column shows why sexual reproduction is a powerful mechanism for perpetuating a species. Both parents are heterozygous at this locus, and both will pass down either a 1 or a 0 with equal probability. Thus the possible values for the child at this locus are 00, 10, 01, or 11. There is a 25% chance that the child will be 00 and be healthier than either of its parents. Most likely (50%) it will also be heterozygous, either 10 or 01, and in 25% of the cases it will be homozygous mutant.
Note that mutations become fixed only when every individual is a homozygous mutant at some locus. As long as any individual retains a wild gene at a locus there is a chance the 0 will spread to one or more offspring and potentially even eliminate the mutation.