There can be various lines on a map, but the ones you are probably thinking of are 'latitude' and 'longitude'.
Parallel lines found on a map correspond to latitude.
longitude
On a map, longitude lines go up and down, AKA vertically. Latitude lines are horizontal lines on a map.
The lines that are perpendicular to the latitude lines on a map are called longitudinal lines. There are 24 of them, each representing 15 degrees of change.
Isotherms and they are lines on a map that connect areas with the same surface temperature.
The lines that intercept latitude lines are lines of longitude.
Topographical lines
"contour lines"
Contour lines: These lines connect points of equal elevation on a map and help depict the shape of the land surface. Latitude and longitude lines: These lines form a grid on a map to establish the precise location of a point on Earth's surface. Borders: These lines define the boundaries between different countries, states, or regions on a map.
The latitude lines printed on a map will depend on the scale of the map. A map of the Earth will probably have latitude lines printed every 15 or 30 degrees; a map of the United States will have latitude lines printed every 5 or 10 degrees.
Contour lines show levels of elevation, where there are hills and valleys on a map
The lines are parallel on the map are called Latitudes.