What does it mean when a trait is "80% heritable"?

When a trait is called "80% heritable", it does not mean that 80% of you comes from your genes. Heritability is a statistic that estimates how much of the variation in a trait across a population is due to genetic variation between individuals in that population. It measures a fraction of variability, and that is not the same as saying that this fraction of an individual's trait is caused by genetics. It is incorrect to say that because the heritability of personality traits is about 0.6, 60% of your personality is inherited from your parents and 40% comes from the environment.

Heritability describes a population in an environment, not a person. It is specific to a particular population in a particular environment, and it can change without any genetic change occurring, for instance when the environment starts contributing more variation. High heritability also does not necessarily mean that a trait is not very susceptible to environmental influences. And it cannot take into account factors that are the same for everyone, like no one having access to a particular antibiotic, or everyone drinking coffee.

Where do the numbers come from? In humans, mostly from twins. Identical twins are on average twice as genetically similar as fraternal twins, so a crude estimate is twice the difference in their correlations. Breeders use heritability for something concrete: if selected parents average 120 kernels per ear against a population average of 100, and heritability is 0.5, the next generation averages 10 additional kernels, so 110.