Complex networks have been successfully used to describe the spreading of a disease in populations of interacting individuals. Conversely, pairwise interactions are often not enough to characterize processes of social contagion, such as opinion formation or the adoption of novelties, where more complex dynamics of peer influence and reinforcement mechanisms are at work. Here we introduce a high-order model of social contagion in which a social system is represented by a simplicial complex and the contagion can occur, and with different transmission rates, not only over the links but also through interactions in groups of different sizes. Numerical simulations of the model on synthetic simplicial complexes highlight the emergence of novel phenomena such as the appearance of an explosive transition induced by the high-order interactions. We show analytically that the transition is discontinuous with the formation of a bistable region where healthy and endemic states co-exist. Our results represent a first step to understand the role of high-order interactions in complex systems.