People who are responsive are alert and aware — they've giving responses. The least responsive people in the world are people in deep comas.
Responsive has several meanings, but they're very similar. If someone just came out of a coma and starting saying anything at all (or even started blinking), you'd be happy at how responsive they are. A person who has enthusiasm is more responsive than someone who is quiet and seems bored. Things other than people can be responsive too: a plant is responsive to sunlight, and the fire department is responsive to a fire. Anything that is alert and quick to react is responsive.