They are imaginary lines that create a system of coordinates on the surface of the Earth (other spherical objects). The parallels (or latitudes) measure the angular distance from the equator which is the line that is in the plane perpendicular to the Earth's axis of rotation. The North Pole is 90 degrees to the North of the equator and the South Pole is 90 degrees South.
The Meridians (or longitude) run from Pole to Pole. The one going through Greenwich - in London and home of the Royal Observatory) is designated the Prime Meridian. Other meridians measure the angular distance from the Prime Meridian in the Eastward or Westward direction. There are 180 degrees to the East of the Greenwich Meridian and 180 to the West. Actually, that is not strictly true because 180 E and 180 W are the same meridian on the opposite side of the Earth from Greenwich. That meridian forms much of the International Date Line.
The equator is parallel not meridian
The only lines that can run parallel to the Prime Meridian on any map are other meridians of longitude, and the only map on which they can be printed parallel to it is a Mercator Projection. They are not really parallel to the Prime Meridian.
parallel
Meridian
Nothing is parallel to any meridian. The equator is a parallel of latitude, and is parallel to all the other parallels. This is a big part of the reason that, collectively, they are called 'parallels'.
All 'lines' of latitude are parallel to all others.No meridian of longitude is parallel to any others.-- All 'lines' of latitude are parallel to all others.-- No meridian of longitude is parallel to any other one.
It is a parallel. It is parallel to the equator.
The equator is the parallel of zero latitude.
Parallel: 0o latitude
parallel
Vertical lines parallel to the prime meridian are lines of longitude.
There are no geographic lines that are parallel to the Prime Meridian. Technically, every meridian of longitude is parallel to every other meridian of longitude, but only over an infinitesimal distance north or south of the equator. I'm quite sure that's not what you're looking for.