Rubidium was discovered in 1861 by Robert Bunsen (1811-1899) and Gustav Kirchhoff (1824-1887) in Heidlelberg, Germany. It was discovered in the mineral lepidolite with the help of a spectroscope. The name 'Rubidium' comes from the latin word 'rubidius', which means 'dark red'.
The two scientists heated the then newly discovered lepidolite mineral (discovered in the 1790's by the Jesuit priest Abbé Nicolaus Poda (1723?-1790) of Neuhaus, Germany) and gazed at it through a spectroscope. Rubidium as we know it now is not in the chemical formula of lepidolite; it's just a possible product of impurities in the mineral. So one of the times when Bunsen and Kirchhoff looked through the spectroscope, they discovered two new lines in the spectrum, which were dark red. So they named the new element 'rubidium' because of the dark red colors of the lines.