Overview and images of basalt as a rock type are here: Basalt
Olivine basalt is basalt with olivine phenocrysts. Phenocrysts are mineral grains that are substantially larger than the groundmass surrounding them.
If the olivine grains are large enough they may be used as gemstones. Olivine as a gemstone is often named peridot(e). Olivine in basalt usually contains more Mg than Fe. Its chemical composition is (Mg,Fe)2SiO4
Olivine is denser than most other minerals in basalt and it is also one of the first to start crystallizing. Hence, it often sinks, if it has room to do so, and forms basalts that are abnormally enriched in olivine in the lower part of lava flows for example. Olivine crystals in this case were already formed before the lava poured out of the volcano because phenocrysts need time to grow. Rapid cooling in subaerial conditions would not allow it to grow as large as the crystals shown on the photo below which is a piece of olivine basalt from Oahu, Hawaii.
Olivine sand is a disintegration product of rocks with similar composition.
Olivine basalt from Oahu, Hawaii. The width of the rock is 6 cm.