Cultural evolution allows ideas and technologies to accumulate across generations, reaching their most complex and open-ended form in humans. While social learning enables the transmission of such innovations, the cognitive processes that generate them remain poorly understood. Classical theories typically treat innovation as random variation, a simplification insufficient for explaining the complexity of human cultural evolution. We propose that semantic knowledge-the associations linking concepts to their properties and functions-guides human innovation and drives cumulative culture. To test this, we combined an agent-based model, which examines how semantic knowledge shapes cultural evolutionary dynamics, with a large-scale behavioral experiment (N = 1,243) testing its role in human innovation. Across both approaches, we found that semantic knowledge directed exploration toward meaningful solutions, enhanced innovation success, and enabled generalization from prior discoveries. Moreover, semantic knowledge interacted synergistically with social learning to amplify innovation and accelerate cumulative cultural change. In contrast, experimental participants lacking access to semantic knowledge performed no better than chance, even when social learning was possible, and relied on shallow exploration strategies for innovation. Together, these findings suggest that semantic knowledge is a key cognitive process underpinning human cumulative culture.