What do the horizontal lines in a P-V phase diagram mean?
the graph is trying to show three things (pressure, density and temperature)  in 2D. 



The yellow portion shows the super critical fluid of $\ce{CO2}$.

The blue portion liquid $\ce{CO2}$

The light green portion shows the gas phase for $\ce{CO2}$.

The horizontal lines are called "tie lines." The two phases at the ends of the tie lines are in equilibrium. 

If you follow the line for say for 12 $^\circ$C, from the degree notation there is at first one phases, a gas phase.

Now when you reach the dotted curve there are two phases a gas phase and a liquid phase which are joined by a horizontal tie line. 

The whole thing is a lot easier to figure out with a more traditional phase diagram. 

 

Found above on page:
https://www.engineeringtoolbox.com/CO2-carbon-dioxide-properties-d_2017.html