The cosmological constant problem remains one of the most significant unresolved issues in modern theoretical physics. Quantum field theory predicts vacuum energy densities that exceed the observed cosmological constant by roughly 122 orders of magnitude, yet no universally accepted mechanism explaining this discrepancy has emerged. This paper proposes a structural interpretation of the cosmological constant within the Breathing Universe Model (BUM), where the vacuum is treated as a structured dynamical medium governed by tension balance. Central to the framework is the zero-line equilibrium, defined as the cancellation between complementary expansive and contractive vacuum tendencies. The analysis argues that exact cancellation of vacuum contributions can occur only within finite coherence domains. Two natural limits therefore arise: a minimal coherence scale associated with Planck-scale vacuum structure and a maximal coherence scale determined by the cosmological horizon. Because the vacuum cannot maintain perfect balance across the entire universe simultaneously, a small residual imbalance remains. This residual vacuum tension produces an effective cosmological curvature that scales inversely with the square of the horizon radius. Expressed in Planck units, the resulting relation naturally reproduces the observed hierarchy between Planck-scale vacuum energy and the measured cosmological constant. Within this interpretation, the cosmological constant does not represent a fundamental microscopic vacuum energy density. Instead, it appears as the horizon-limited remainder of an asymptotic zero-line cancellation process in a structured vacuum medium. The observed value of Λ therefore reflects the enormous hierarchy between the minimal coherence scale of the vacuum and the maximal coherence domain defined by the cosmological horizon. The framework remains compatible with standard ΛCDM cosmology and does not modify the Friedmann equations governing cosmic expansion. Rather, it provides a structural explanation for the small magnitude of the cosmological constant by linking it to horizon-limited vacuum coherence.