The origin of the word abstinence is tied to ideas of self-restraint and self control. Abstaining from eating certain foods, drinking alcohol or taking other drugs, or engaging in sexual contact is understood as a choice one makes.
In the context of sexuality, abstinence generally refers to not engaging in any form sexual behavior. Whether or not this includes 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 follows will include details about what counts and doesn't count as sex.
Someone who is abstinent is often said to be "practicing" abstinence or choosing it. Being abstinent doesn't necessarily mean that an individual has a particular political or religious reason for not having sex. It also doesn't imply that one has never had sex or that one intends to avoid sex in the future.
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.