It is used in taxation where the personal liabilities of the individual increase with income where the basic principle is that- the individual with higher income and more assets should pay more tax.
There is another method used in such calculations called horizontal equity, where all citizens are subject to the same absolute amount of taxes where the state considers and guarantee equal legal rights to all and imposes the same liability to all.
Vertical is used along with the ability to pay which means the total tax paid by a person should be proportional to the total wealth created through alternative asset class, illiquid assets, and average stock market return UK or others - as per the capacity one may have to bear the tax burden.
It is followed in the US where the tax on earnings up to $8,025 = 10%, $24,525 = 15% and $49,100 = 25%.
There are other methods like proportional equity where all individuals pay the same rate and as the wealth of a person increases, the absolute amount of the tax liability increases at the same rate.
Progressive is the method where the percent of income increase with wealth and regressive where low earners pay more to the state.