The variety of leopard gecko patterns (known as morphs - that is, types that are visually distinct from each other because of color and pattern variations) available today is truly staggering. If you've only ever seen the standard 'wild' leopard gecko, then you owe it to yourself to check out some pictures of spectacular morphs such as the Diablo Blanco, Super Hypo Carrot Tail, or Rainwater Mack Snow. They look as amazing as their names suggest.
Seeing these leo morphs might well get you interested in breeding leopard geckos to produce them, and why not - it's a great hobby. However, the sting in the tail is that doing this requires you to become an amateur geneticist, as otherwise you simply won't be able to understand well enough how to get the results you want.
The first thing to learn is some frequently used terms. Phenotype, for example, refers to the traits that a creature has and is showing. Genotype on the other hand refers to the traits that a creature is carrying but not necessarily showing. A couple more terms: heterozygous (or just 'het' for short) refers to a creature that is carrying one copy of a specific recessive trait and one copy of a normal trait. Homozygous is the opposite: it refers to a creature that is carrying two copies of the same trait.
Ok, let's now use those terms: a leopard gecko of the albino phenotype is homozygous. It looks like an albino because it carries two copies of the recessive albino trait. A het albino leo, on the other hand, won't look like an albino, as it carries only one copy of the recessive albino trait. It's important to know when you have a leo of the het albino phenotype however, as otherwise you might just think it's a normal wild-type leopard gecko, and miss the opportunity to breed it with another het albino to try to produce a homozygous albino.
If you have two het albinos - a male and a female - then each of their children has a 25% chance of being a homozygous albino, and therefore looking like an albino. If you have two albinos, then all of their children will be of the albino phenotype too. Simple enough?
The other important concept to grasp is that of 'line bred' traits. Line breeding refers to selecting leos with a certain trait that's a little different from the norm and breeding them together over successive generations to emphasize that trait. The tangerine morph, for example, was developed by picking a male and a female leopard gecko that both happened to have a slightly brighter background color than usual and breeding them together, then picking the brightest of their children and breeding them together, and so on and so on over a number of generations. Over time a really bright tangerine morph was produced.