The influence of symmetry breaking in a planar metamaterial on transparency effect is numerically investigated. The planar metamaterial's cell is formed by three parallel metal wires. From numerical simulation results, we can see that the transparency effect results from the asymmetric coupling between the cut wires. The excited mechanism of the transparency effect is further analyzed by using the hybridization concept. It is found that the coupling fields between the cut wires play key roles and lead to the spectral splitting of the resonance, i.e., the classical electromagnetically induced transparency effect. The metamaterial sensor based on the refractive index variation of the surrounding material is also numerically demonstrated and yields a sensitivity of 9.47 mm/RIU and a figure of merit of 13.5. In addition, the spectral response of the metamaterial is quantitatively described via the "three-particle" model. The analytically calculated results of the model show a good agreement with the simulation results.