Other forms: irritated, irritating, irritates
To irritate somebody is to make them slightly angry, over and over. Small, repeated, and cumulative.
The repetition is the point, since a single act annoys and a repeated one irritates. It also has a physical sense, and something that irritates the skin makes it red and sore, which is why cosmetics are tested for it. Both meanings come from the same idea of persistent rubbing. The adjective irritating describes the cause, irritated the sufferer, and irritable a person who is easily set off.
To irritate was to excite. Latin irrītō meant to stir up, to incite or to stimulate, so the annoyance is English narrowing a much broader word.
Latin
irrītātus
English, today
irritate
Built from
Latin irrītātus, perfect passive participle of irrītō (“excite, irritate, incite, stimulate”), see -ate.
Etymology from Wiktionary, CC BY-SA