1) No more meticulous bookkeeping for filing income tax forms every April 15th. That right there saves Americans possibly US$500 BILLION per year in compliance costs.
2) American citizens get 20-25% bigger paychecks from the employer due to no more tax withholding.
3) American citizens can put their deposit their paychecks into bank or investment accounts with no tax consequences. That means no more incentives to either participate in the underground economy or funnel out money to offshore financial centers, since there are no more income taxes to dodge! 
4) As a result of #3, most of that US$15 TRILLION in American-owned liquid assets now out of the US financial system for tax avoidance reasons returns, essentially the world's biggest "private bailout."
5) Also as a result of #3, Americans can confidently save up for a retirement nest egg or save up for a big-ticket item purchase. It also means Americans can put down larger-sized down payments for loans, which means loans are far more likely to be paid back in full.
6) Because we no longer impose taxes on earning money, there will be a GIGANTIC land rush of foreign money into the USA--an amount that could reach WAY over US$10 TRILLION in addition to the repatriation of American-owned liquid assets mentioned in #4. It also means foreigners will rush to open US subsidiary operations of foreign companies, too.
In short, just the potential of over US$25 TRILLION in repatriated and new liquidity entering the US financial system is a huge reason FairTax should replace the broken-down income tax system.