It is the pull of the Moon's gravity on the Earth that holds our planet in place. Without the Moon stabilizing our tilt, it is possible that the Earth's tilt could vary wildly. It would move from no tilt to a large tilt. The consequences of a second moon orbiting the Earth depend on how massive that moon is and how far from the Earth it orbits. The most obvious effect would be that the ocean tides would be altered. Tides could be either smaller or higher and there could be more than two high tides per day.