In simple mendalin genetics - a trait is governed by a particular gene pair.
The gene pair is said to be homozygous (or homo) if both genes in the gene pair are the same. The gene pair is said to be heterozygous (or het) if the two genes in the gene pair are different.
Most of the traits for which the terms are used have a dominant/recessive relationship. Usually the "normal" gene is dominant and the "morph" gene is recessive.
What this means - if both genes in the gene pair are the same and "normal" - the snake has the "normal" trait.
If the gene pair is heterozygous with a "normal" and "morph" gene - the snake displays the "normal" trait because it is dominant.
If both genes in that pair are the "morph" gene - then the snake displays the morph.
This snake of mine is heterozygous for amel albinism:

It looks like a normal banded california kingsnake, and the only way I know it is het for amel is because it has an amel mother, so it had to get an amel gene from the mother. It got a normal gene at that gene pair from the father, which is dominant - and that's why she looks normal. But she carries the amel gene and could produce some amel babies if mated with another snake that carries the ame; gene.
Double Het is a snake that has two gene pairs that are heterozgous. For example - the gene that causes ghost is a different gene pair than the gene that causes amel.
So if you bred a ghost with an amel, the hatchlings would be normal looking (not express ghost or amel) but carry both genes.
Not all traits are simple dominant/recessive - but many are.
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3.6 L. getula californiae (Cal. King)
1.1 L. getula nigrita (MBK)
1.0 Pantherophis guttatus guttatus (Corn)
1.0 Thamnophis sirtalis fitchi (Valley Garter)
1.0 Boa constrictor constrictor (suriname, fostering/rescue)
3.3 Elgaria multicarinata multicarinata (Cal. Alligator Lizard)