Equality and equity are two different methods for establishing fairness. Equality means that everyone is treated the same, whereas equity is giving every person what they need to be successful.
Economically, an example of equality in America would be charging each citizen a flat tax of 25%. In this example, if you earn only $20,000 a year, you pay 25%, and if you earn $1 million a year, you pay 25%. This is fair, in a sense, but the millionaire still has way more money than the person who makes $20,000 a year, even though they paid the same tax rate.
An example of equity, on the other hand, would be to charge the first person in this scenario a far lower tax rate, while the millionaire gets charged a much higher tax rate. It's not equal, exactly; rather, it serves to "level the playing field."
Another example would be in a classroom. At school, everyone learns very differently. Some people need a lot of practice to study for the test, while some people grasp the concept easily right away. Equality would be the teacher giving every student five minutes of extra help, regardless of whether it's too much or not enough. Equity would be the teacher giving extra help to people who need it and not spending as much time with the students who already understand.
When viewing this question in the context of the United States, examples can be found in racial, gender, and economic privilege. Equity is the idea that the people who need more help should get more help, even if that means that those who are fortunate get no extra help at all.