The Concept of Equity is explained below:

Equity represents that the principle of taxation which emphasizes fairness or just the sacrifice, which is everyone must pay the tax depending on his/her ability. Hence if a person earns higher income, she/he should be subjected to the higher tax rate. Thus, for example one person is earning Rs. 2,000 per month should sacrifice 10% of his/her income as the taxes paid to the government (i.e. Rs.200), whereas the person who is earning Rs. 200,000 should give 60% of his/her income as the taxes (i.e. Rs. 120,000). In the absence of such progressive taxation, the rich person would have also paid the 10% of the income tax rate (which becomes Rs. 20,000). The progressive taxation, in which the tax rate raises as the income increases, is an application of the vertical equity of the principle which espouses the Robinhood approach of taking money from rich and distributing it to poor people. While controversial, vertical equity principle in the taxation is applied in one way or the other in most of the countries across the world. 

Horizontal Equity is explained as follows:

A less controversial principle relates to the horizontal equity which says: identically well-off people should be taxed similarly, which means no discrimination due to race, caste, religion gender, etc. There are number of examples, though, of violation of this principle and often one comes across the individual belonging to the particular community or grouping enjoying certain economic privileges not enjoyed by the similarly endowed individual of another community or grouping.

We now turn to towards efficiency dimension, which concerns distortionary effects of the taxation, especially the possible negative effects on the private sector behaviour and incentives. The more distortionary a tax, the higher is the efficiency concerns surrounding it.