The first thing is to become familiar with a few terms commonly used in genetics !

Genes
The gene is defined as the unit of inheritance. A gene is actually a sequence of DNA contained by and arranged linearly along a chromosome. Genes are responsible for each trait of your cat to be inherited such as eyes color, coat color and so on. They are always present in pairs: each pair contains the informations about the inheritance of a certain trait. The gene pairs about the same trait are called alleles: they contain informations about the same trait and they can contain the same info or different ones.
For example one allele may contain informations for blue eyes, while the other allele may contain informations for green eyes.

Homozygous and Heterozygous
When alleles contain the same informations on a certain trait your cat is called Homozygous for that trait (ie both alleles contain infos for blue eyes).
If alleles contain different informations on a certain trait your cat is called Heterozygous for that trait (ie an allele contain infos for blue eyes, while the other allele contain infos for green eyes).

Phenotype
It’s simply HOW your cat looks, so it is the visible effect of your cat genes.

Genotype
It’s the summary of all the genetic informations in your cat genes. So the visible ones and the not visible ones that can be still passed to the progeny.

Dominant and Recessive
If both alleles contain the same informations about a certain trait we will have no doubt about the phonotype: if both alleles contain infos for blue eyes we will get a cat with blue eyes.
But what if alleles contain different infos about the same trait?
One of the alleles will be “dominant” on the other one (called “recessive”) and only the information of the dominant allele will be visible in the cat phenotype.
We can explain how it works with the longhair and shorthair gene.
In cats the gene referred to as “L” is the one responsible of a short or long coat.
The shorthair feature is DOMINANT and referred to as L
The longhair feauture is RECESSIVE and referred to as l
SO we can have 3 different situations:
1
The cat is homozygous for the coat feauture and has 2 alleles L (L L for shorthair). In this case the cat is homozygous for this trait and has 2 dominant alleles. This trait expression (phenotype) is a shorthair cat.
2
The cat is homozygous for the coat feauture and has 2 alleles l (l l for longhair). In this case the cat is homozygous for this trait and has 2 recessive alleles. This trait expression (phenotype) is a longhair cat.
3
The cat is etherozygous and has 2 different alleles L and l (one for shorthair and one for longhair). In this case the cat has a dominant allele and a recessive one. The gene expression (phenotype) will be a shorthair cat because the dominant allele will cover the expression of the receccive one. We will have a shorthair cat that will CARRY the longhair trait as it will be inherited by part of the progeny.