What does the statement mean "50% of happiness is determined by genetics"?
The statement 50% of happiness is determined by genetics is presumably talking about heritability estimates.

It is probably talking about the percentage of variance explained by genetics. 

These estimates are commonly estimated using twin studies. For example, you administer a survey to people that ask a bunch of questions about how happy they feel. There are a variety of measures (e.g., life satisfaction measures, quality of life measures, measures of tendencies to experience positive and negative emotions). If you administer these measures to twins, some of which are fraternal and some of which are identical, you can compare the degree to which the overlap in happiness scores increases in the identical over the fraternal twins. 

A wide range of theories of well-being suggest that most people are happy most of the time. There is also theory to suggest that a person's emotional tendencies (e.g., see neuroticism, extraversion, well-being, and so on) are quite stable over long periods of time (i.e., over many years). So this does suggest, that at the very least, it is unusual for someone's emotional tendency to change dramatically over time.