New high-resolution visible emission spectra of the MgH molecule have been recorded with high signal-to-noise ratios using a Fourier transform spectrometer. Many bands of the A 2Pi-->X 2Sigma+ and B' 2Sigma+-->X 2Sigma+ electronic transitions of 24MgH were analyzed; the new data span the v' = 0-3 levels of the A 2Pi and B'2Sigma+ excited states and the v''=0-11 levels of the X 2Sigma+ ground electronic state. The vibration-rotation energy levels of the perturbed A 2Pi and B' 2Sigma+ states were fitted as individual term values, while those of the X 2Sigma+ ground state were fitted using the direct-potential-fit approach. A new analytic potential energy function that imposes the theoretically correct attractive potential at long-range, and a radial Hamiltonian that includes the spin-rotation interaction were employed, and a significantly improved value for the ground state dissociation energy of MgH was obtained. The v''=11 level of the X 2Sigma+ ground electronic state was found to be the highest bound vibrational level of 24MgH, lying only about 13 cm(-1) below the dissociation asymptote. The equilibrium dissociation energy for the X 2Sigma+ ground state of 24MgH has been determined to be De=11104.7+/-0.5 cm(-1) (1.37681+/-0.00006 eV), whereas the zero-point energy (v''=0) is 739.11+/-0.01 cm(-1). The zero-point dissociation energy is therefore D0=10365.6+/-0.5 cm(-1) (1.28517+/-0.00006 eV). The uncertainty in the new experimental dissociation energy of MgH is more than 2 orders of magnitude smaller than that for the best value available in the literature. MgH is now the only hydride molecule other than H2 itself for which all bound vibrational levels of the ground electronic state are observed experimentally and for which the dissociation energy is determined with subwavenumber accuracy.