Usually refers to not engaging in any form sexual behavior although whether or not abstinence includes abstaining from masturbation is a matter of interpretation. Usually if one is choosing to be abstinent as part of a religious or political choice, the guiding philosophy one comes from will specify the details of how to abstain.
Someone who is abstinent is often said to be "practicing" abstinence or choosing it. Many people try to practice abstinence until they are in a long term committed relationship or married. Others choose to be abstinent for a period of time in their lives after they have already explored solo and partner sex.