It's been years since I learned about this so I'll probably be wrong to some degree but:
We have recessive genes in our DNA that don't affect us (put simply). When you mate with someone you pass on those recessive genes, if your mate happens to have the same recessive gene there's a good chance your offspring will have that trait. The problem with inbreeding is that there's a very high chance your family will have the same recessive genes as well, which can be anything from hair color to severe mental and physical defects.
Yeah, that's accurate.
It's not that incestuous families have more mutations than other people. The mutations are caused by failed DNA transcription, where genes can have sections of DNA written out wrong (imagine a G becomes a C, or even the G is forgotten entirely and everything shifts along one space).
These mutations happen at the same rate in all people, and hereditary genetic diseases crop up when a love cell mutates and then fertilises. Now the child has that mutant gene and can pass it on.
As Steve says though, usually your partner has a wider range of genes. And most mutant genes are recessive, so your partners correct copy takes priority over the mutant one and the child is born healthy (but still has a copy of the mutant gene to pass on).
But when the partners are from the same family, and especially same mother and father, they have very very similar genes, and can both have the mutant gene, which their child expresses.
As Bloody Mary and Conan pointed out the cleanest way to show an incestuous non-sibling relationship is to add the repeated box in, with no other connections to it.
This is the cleanest way, but not always the clearest, as someone reading the tree may assume it is two different people.
This also works for individuals who procreate with multiple members of the family.
So if [John Smith] has a child with both cousins [Jane Doe] and [Joan Doe] then you can put [John Smith] in twice, rather than trying to get both the cousins close to him or having long lines connecting him to them.
