A person who believes that an authoritarian state is righteous and justified as long as it calls itself communist (even if it's not), examples being the USSR, North Korea, China, and oddly the current capitalist Russian federation. You can find a more in-depth answer here.

Someone who sees through cold-war anticommunist propaganda and defends the anti-imperialist and massively progressive Actually Existing Socialist states (USSR, China, Cuba, Vietnam...) instead of belonging to the "compatible left" that doesn't actually have a history of successful struggle against capitalism and imperialism.

People will be called tankies for defending the socialist figures and projects which get vilified in western discourse precisely because of their success against capitalism and fascism (Fidel, Lenin, Mao, Ho Chi Minh), whereas anticommunists will only praise historical figures and projects who failed (Allende, Rojavas, Spanish anarchists) because their metric is not actual improvements to quality of life of people but ideological purity.

Tankie started out as a pejorative word against communists with the attempt to associate them with militarism. Notice how other leftists don't call liberals "dronies" for supporting Obama despite the drone attacks on civilians in the middle east, don't call fascists or Nazis "campies" despite the extensive usage of concentration camps, and don't call capitalists "colonies" despite the widespread colonialism, such violent terms are only reserved to socialists. I consider myself a communist and I reclaim the label "tankie", since it was actually Soviet tanks (T-34s mainly) which destroyed Nazism and saved hundreds of millions of lives in Europe from extermination.