Your celestial meridian is an imaginary line that begins at the northern point of your celestial horizon and travels over your head, through your zenith, and down to the southernmost point of your celestial horizon.
The line makes a hemispherical arc from north to south through your zenith.
There is no special term for the east-west line through your zenith.
Because it is fixed to the local horizon, stars will appear to drift past the celestial meridian as the earth spins.