It means "to irritate" or "greatly bother".

It refers to the creepy and intensely uncomfortable feeling you get when you bite into something that makes your teeth squeak or scrape--like some of the sensations you get when a dentist is cleaning your teeth, for example. It is related to the phrase "like the sound of a fingernail scraping on a blackboard." It is a very old, classic idiom--it appears in the 1611 King James Version of the Bible in English. Ezekiel 18:2, "What mean ye, that ye use this proverb concerning the land of Israel, saying, The fathers have eaten sour grapes, and the children's teeth are set on edge?" Since you speak Spanish, I'm curious to see how the same verse is translated in Spanish. RVR 1960: "Los padres comieron las uvas agrias, y los dientes de los hijos tienen la dentera?" And now let me check a dictionary: yes, the first meaning shown for "dar dentera" is "set your teeth on edge."