In plasmonic Fano resonance, the interaction between a discrete plasmonic mode and a continuum of plasmonic mode gives rise to an asymmetric line shape in the scattering or absorption spectrum, enabling a wide range of applications such as sensing, switching, and slow light devices. Here, we establish a theoretical solution in the framework of temporal coupled-mode theory (TCMT) to study the three-dimensional (3D) and two-dimensional (2D) Fano resonances induced by strong coupling between metal hole (MH) and split ring resonator (SRR) array. We first separately analyze the transmission spectra of the MH array and SRR array under different polarized light excitation. We further investigate the electromagnetic field and charge density distribution corresponding to the resonant modes at the peak or valley wavelength of the transmission spectrum and figure out the electric/magnetic dipole feature of these resonance modes. We then establish a theoretical solution by TCMT for Fano resonances arising from the coupling of these modes. The calculated transmission spectrum is closely matching with the numerically simulated transmission spectrum for these Fano resonances in the MH-SRR array, which effectively elucidates that the asymmetry of the Fano resonances is caused by the coupling between bright and dark plasmonic modes involved in the two structures. Our results can help to understand the profound physics in such coupled plasmonic systems.