Which direction do parallels run and what do parallels measure?

Answer 1

Parallels are lines running in the same direction, but that doesn't tell you which direction that is. Parallels don't measure anything.

Answer 2

Since this is in the geography section I will assume you mean on a globe, so I suppose on the earth too, that would be latitude lines, since longitude lines are not parallel, but join at the poles. Latitude lines never meet. And they measure distance from the equator.

Answer 3

Parallels run east/west and measure latitude. Latitude is the degrees north or south of the equator.