The discovery of four large moons orbiting around Jupiter by Galileo Galilei four hundred years ago spurred the Copernican Revolution and forever changed our view of the Solar System and universe. Today, Jupiter is seen as the archetype for giant planets in our Solar System as well as a paradigm for the numerous giant planets known to orbit other stars. In many respects, and in all their complexities, Jupiter and its diverse satellites form a mini-Solar System.In the framework of the ESA "Cosmic Vision" programme, the JUpiter ICy moons Explorer (JUICE) mission has been selected as the L-class mission to be launched in 2022, with an arrival at Jupiter planned in 2030. JUICE is an ESA-led mission arising from the reformulation of the EJSM-Laplace mission, which was instead an ESA-NASA project. Here we discuss the main scientific aspects of the current JUICE mission concept. The overarching theme for JUICE is: "The emergence of habitable worlds around gas giants". The focus of JUICE is to characterise the conditions that may have led to the emergence of habitable environments among the Jovian icy satellites, with special emphasis on the three ocean-bearing worlds, Ganymede, Europa, and Callisto. Ganymede is identified for detailed investigation since it provides a natural laboratory for analysis of the nature, evolution and potential habitability of icy worlds in general, but also because of the role it plays within the system of Galilean satellites, and its unique magnetic and plasma interactions with the surrounding Jovian environment. For Europa, where two targeted flybys are planned, the focus will be on the chemistry essential to life, including organic molecules, and on understanding the formation of surface features and the composition of the non water-ice material, leading to the identification and characterisation of candidate sites for future in situ exploration. Furthermore, JUICE will provide the first subsurface observations of this icy moon, including the first determination of the minimal thickness of the icy crust over the most recently active regions. The study of the diversity of the satellite system, important also to shed light on their origins, will be completed with twelve targeted flybys of Callisto and additional information gathered remotely on Io and smaller moons. Focused studies of Jupiter's atmosphere and magnetosphere, and their interaction with the Galilean satellites, will further enhance our understanding of the evolution and dynamics of the Jovian system. The circulation, meteorology, chemistry and structure of Jupiter will be studied from the cloud tops to the thermosphere. These observations will be attained over a sufficiently long temporal baseline with broad latitudinal coverage to investigate evolving weather systems and the mechanisms of transporting energy, momentum and material between the different layers. The focus in Jupiter's magnetosphere will include an investigation of the three dimensional properties of the magnetodisc and in-depth study of the coupling processes within the magnetosphere, ionosphere and thermosphere.