Vertical Equity
  
Generally speaking, "vertical" means up and down. Like...the x-axis on a graph is horizontal, and the y-axis is vertical. Your car should stay relatively horizontal if you're driving over a bridge. If it goes vertical, you're in trouble.
For the term "vertical equity," the vertical part refers to the amount someone makes. Usually, when the phrase comes up, you're talking about tax rates.
The main question is whether people at higher levels of income should pay higher, lower, or the same tax rates as people with lower levels of income. The question gets at the "vertical equity" of the tax rate.
A tax system that is vertically equitable would charge higher rates for higher levels of income. Make $25,000? You pay a 7% income rate. Make $50,000? You pay 10%. Make $100,000? You pay 12%. That would represent a vertically equitable system.