Do some light research on how taxes work. But basically, when you go up a tax bracket, only the income over that threshold is at the higher rate.

So, (brackets made up for easy and clear math), let's say this was the tax rate set up.

0-$10,000=0%

10,001-20,000=5%

20001=30,000=10%

30001=40,000=20%

Someone making $9000 pays $0 (0% of 9k)

Someone making $20,000 does not pay $1000, which would be 5% of that 20k. The first 10k is at the 0% rate, and only everything over that is at the 5% rate, so they would pay $500. (0% of 10k + 5% of the second 10k--the salary from $10000 to $20000). Someone making $30k would pay $1500 (0% of 10k, 5% of the second 10k, and 10% of the third $10k).

And so on.

This means that making more money can never cause you to take home less, because only the money over the next bracket leve is at the higher rate. So in my example, if the raise bumped you from $30k to 30,500, $500 of your money would be in the higher 10% tax bracket. But you'd still only pay $1500 on that first $30,000, and then that new $500 would be taxed at 20% ($100). So before the raise you took home $28,500 ($30,000 minus $1500) and now you take home $28,900 ($30,500 minus $1600). So the raise still causes you to come out ahead.

Hopefully that helps.