The CDC page he linked to defines "eliminated", as does his comment: "absence of continuous disease transmission for greater than 12 months". You can have outbreaks of a disease that have been eliminated from a population: the disease can be reintroduced from some other population. But what you don't have is person-to-person transmission within the population.
Measles History from the CDC: https://www.cdc.gov/measles/about/history.html