Quantum computing is a rapidly evolving field that enables exponential speed-up over classical algorithms. At the heart of this revolutionary technology are quantum circuits, which serve as vital tools for implementing, analyzing, and optimizing quantum algorithms. Recent advancements in quantum computing and the increasing capability of quantum devices have led to the development of more complex quantum circuits. However, traditional quantum circuit diagrams suffer from scalability and readability issues, which limit the efficiency of analysis and optimization processes. In this research, we propose a novel visualization approach for large-scale quantum circuits by adopting semantic analysis to facilitate the comprehension of quantum circuits. We first exploit meta-data and semantic information extracted from the underlying code of quantum circuits to create component segmentations and pattern abstractions, allowing for easier wrangling of massive circuit diagrams. We then develop Quantivine, an interactive system for exploring and understanding quantum circuits. A series of novel circuit visualizations are designed to uncover contextual details such as qubit provenance, parallelism, and entanglement. The effectiveness of Quantivine is demonstrated through two usage scenarios of quantum circuits with up to 100 qubits and a formal user evaluation with quantum experts. A free copy of this paper and all supplemental materials are available at https://osf.io/2m9yh/?view_only=0aa1618c97244f5093cd7ce15f1431f9.