The Meridian is an imaginary Great Circle on the Celestial Sphere that is perpendicular to the local Horizon. It passes through the North point on the Horizon, through the Celestial Pole, up to the Zenith, and through the South point on the Horizon.
Because it is fixed to the local Horizon, stars will appear to drift past the Local Meridian as the Earth spins. You can use an object's Right Ascension and the Local Sidereal Time to determine when it will cross your Local Meridian (see Hour Angle).