A zero line is graphically explained as
y
always equals zero (0), and is usually relevant when
you're talking about a value that changes with time or with some other
monotonically increasing
input value.
If you take all of the values and put them in order into a time-series, it is said that the time-series "crosses" the zero line when the value has either become negative having previously being positive, or positive having previously being negative.
As an example, a sine wave periodically crosses the zero line. As its input values continue to increase, it oscillates around the zero line.
The zero line can also mean the natural resting position
of something which moves around. Like the pendulum on a clock. The zero line is the resting position of the pendulum when the clock is not running.
When the clock is running,
the pendulum swings back and forth across the zero line.
See also: oscillator