Abstinence means avoiding doing something. This can include alcohol, films, games, some types of food, or anything else you choose to abstain from, either temporarily or permanently.
This word is often used to do with sexual abstinence, meaning that you choose not to have sex with anyone. Another word for this is celibacy. There can be many reasons for this, such as not finding someone to marry. Some people decide not to marry, and live in abstinence for their entire lives, for different reasons. The Bible teaches that sex is only allowed in the context of a marriage between a man and a woman, and that we should therefore live in abstinence as long as we are unmarried. It is neither unhealthy nor damaging to live without sex, although it may be felt as a loss.