Dear Marcia,  

When talking about celibacy, as about any vow, you can talk about two different types of faults against it. There are faults that break the vow materially, and there are faults that go against the spirit of the vow - just like a woman who flirts may not have actually broken her marriage vows, but definitely has weakened them and gone against them, and hurt her husband.  

Now, the obligation to chastity binds all Christians. The married abstain from relationships outside of marriage, and the unmarried abstain from intercourse before marriage. There are many other elements in the relationship between a man and a woman besides actual intercourse, but the rightness or wrongness of engaging in them depends on the state of the individuals involved. For example, you have the social kiss and hug that people give each other, and there is nothing wrong with a married man greeting a woman who is not his wife in that way; then there are signs of affection that are appropriate to engaged couples but not earlier; and those that only the married couple should allow themselves with each other.  

Apply this to the priest. A priest takes the vow of celibate chastity in order to give himself totally to Christ and souls, all his mind, heart and will. It is eminently positive in its intention. Celibacy means abstaining from marriage. A social kiss or hug does not break his vow. But spending a little more time with a particular woman, growing familiarity in their dealings, thinking of her all the time, behaving as a boyfriend would with a girlfriend, dating, etc... are incremental steps which, even though they would be normal in an unmarried man and of themselves would not be sinful, are definitely undermining and going against the spirit of his vows.  

Hope that answers it for you.