To irritate is to cause an unsettling reaction, whether it's of the body or the nerves. You can irritate someone by talking too loudly on your cellphone in public. You can also irritate your skin, causing a rash or redness.
To irritate is to disturb — either physically or psychologically. When you have an allergic reaction to something, you irritate or disturb the body. When you have an allergic reaction to your kid brother, he is probably irritating you with his annoying habits. And what is the result of something irritating? An irritation of course.