Such a concept has many levels we can think of or that we’ve witnessed. On one hand there are those people who will not engage in any sort of penetration - anal or vaginal; but will give other practices such as masturbation and oral sex a go. Then there are those who will only have anal penetration so that technically, they’ll still be virgins on their wedding night. Obviously they equate virginity with possessing an intact hymen, which is a pretty narrow-minded vision of it.
The reasoning behind adopting these versions of abstinence varies greatly. On one hand there are religions that condemn fornication, and so some give it up in order to save their soul. Then there are many who have had negative experiences in the past, or who have great insecurities so they decide to not engage in sex to avoid getting hurt somehow.
Finally there are a great number of people who practice abstinence for health reasons, mainly to avoid sexually transmitted diseases. The huge problem here is that people ignore that many practices which are alternative to penetration, can result in contracting an STD. From oral sex to anal penetration, nothing is 100% sure and so it’s important to always use effective protection from the beginning… or to flat out practice old fashioned abstinence, which means nothing.
You might be pissed off if ever your partner in sex decides to do abstinence. The solution is to offer his/her mild abstinence. But remember, whatever you and your partner in sex decide, you should respect his/her belief and opinion regarding sex if you truly love him/her. If they want to wait until the wedding day, then wait. Great things come for those who wait.