Although the Hall coefficient R(H) is an informative transport property of metals and semiconductors, its meaning in the cuprate superconductors has been ambiguous because of its unusual characteristics. Here we show that a systematic study of R(H) in La2-xSrxCuO4 single crystals over a wide doping range establishes a qualitative understanding of its peculiar evolution, which turns out to reflect a two-component nature of the electronic structure caused by an unusual development of the Fermi surface recently uncovered by photoemission experiments.