Musa paradisiaca is the first Linnean name given to a banana and is therefore technically the "type species" for the genus Musa, despite the developement, in 1955, of an alternative nomenclature system to classify banana cultivars.
The name was coined by Carl von Linné, the father of modern taxonomy, who described the only banana he was familiar with: a specimen cultivated in George Clifford's glasshouse near Haarlem in the Netherlands and famous for being the first banana to flower in Europe. In 1736 Linné, named it Musa Cliffortiana, which is technically a 'pre-Linnean' name. In Species Plantarum, which was published in 1753, he renamed it Musa paradisiaca, in reference to the forbidden fruit of paradise.
Most authorities (e.g. Kew's World Checlist of Selected Plant Families) give Musa paradisiaca or Musa x paradisiaca as an accepted name, thereby perpetuating the practice of giving cultivated bananas Latin binomials. The "x" indicates that Musa paradisiaca is a hybrid and not a species.
Banana cultivar checklist of local names and synonyms