The emic–etic distinction is useful to understand how anthropologists conceptualize ethnographic description and analysis. It comes from the work of Kenneth L. Pike, who draws an analogy between the contrast between phonetic transcription of speech and phonemic analysis of the same utterance (Pike 1967, 37). A phonetic analysis would seek to describe the actual sounds produced by the speaker, including the variations in the pronunciation (for instance, due to dialect, or emphasis). A phonemic analysis would break down the utterance into the ideal units of sound that all speakers of the language possess, the alphabet of the language so to speak.
In the same way, an etic analysis of what people do would describe it in terms of all of its specific observable details. It's the way the world would look to an alien who lands on Earth and witnesses everyday life in progress; they have no background knowledge about what people do every day, so they only can see the physical detail of it. An emic analysis breaks down what people in a community do in terms of the concepts that those people themselves use to understand what they do.
Both emic and etic perspectives are necessary for anthropology, and anthropologists differ on how much they emphasize one or the other. See for instance Mel Spiro's comments on the two perspectives.
Here's another way to think about it: etic is to emic as analysis is to synthesis. The table below lists several emic concepts that Auhelawa people apply to their own lives (on the right) and several etic descriptions (on the left) of what these ideas include, based on Ryan's observation of how Auhelawa people live.
Pike, Kenneth L. 1967. Language in Relation to a Unified Theory of the Structure of Human Behavior. The Hague: Mouton and Co.