Let's think about people.
Let's represent blue eyes, which are recessive, as b. Let's represent brown eyes, which are dominant, as B. Let's say that blue eyes carry a genetic disorder with them, that results in...hmm...let's say spinal deformity. Just for a kick.
We have two people, okay? Both have brown eyes. No chance for genetic disorder, right? Well, not exactly. Let's say that the male (let's call him M) has a genotype of BB. That means that M is homozygous for brown eyes, which means that he carries two alleles (two of the same gene, one from Mum, one from Dad) for brown eyes. And his mate (let's call her F) is heterozygous for brown eyes, which gives her two different alleles, Bb.
Using a Punnet Square, we see that their offspring could result as:
B B
B BB BB
b Bb Bb
Meaning that half of them would be homozygous like their dad, and half of them would be heterozygous like their mum. And yet...all of them would have brown eyes. So we wouldn't know if they were carrying anything in their genes that they could pass on their offspring that would be harmful.
Let's say that M and F had two kids that were both heterozygous, and those two kids decided that they wanted to have kids. Their potential offspring could result as:
B b
B BB Bb
b Bb bb
And here we are already. Third generation, and we may already see our first blue-eyed child...carrying our spinal deformity.
This is why inbreeding is bad. In a large enough population, it is unlikely to find another person carrying the same lethal or deforming recessive. Hence...we go on undeformed. However, with inbreeding, the gene pool is limited, and there are fewer "good" genes to draw upon. There is less variety, so there is more possibility for the "bad" genes to be linked up, resulting in deformities, disorders, etc.
Edit: My Punnet Squares didn't exactly line up. The letters in the topmost rows are supposed to be centered over the outer columns, not over the inner column. But you get the idea.