There are multiple origins and meanings for the name Olivia:
1. Derived from the ancient Greek adjective ὄλβια [ólvia] "happily, richly" means "prosperous; happy; blissful"
2. Italian name, comes from the Latin word oliva - "olive"
The name first mentioned by William Shakespeare at comedy "Twelfth Night, or What You Will". One of the most popular names in English-speaking countries.