What Is Repatriation?  Under U.S. tax law, a company that earns a profit overseas must, in general, pay income tax to the overseas government AND to the IRS if they bring the remaining profit back to the U.S.  The company gets a credit for the foreign income tax paid, but the difference between the foreign tax and the U.S. 35 percent rate must be paid to the IRS.  In practice, deferrals and other tax rules allow companies to keep foreign after-tax earnings locked overseas, but that money generally remains unavailable to be used in the United States.

This is known as a "worldwide" tax system.  All conservatives agree that we should move toward a "territorial" tax system, which most of the developed world already uses.  Under a territorial system, the IRS would only seek to tax those profits earned in the United States.  U.S. companies with foreign-source profits would be free to leave those profits overseas or bring them home without any further tax consequences.  Repatriation is a way of having a territorial tax treatment of overseas income that has already faced foreign income taxation.

Has the U.S. ever tried repatriation before? The U.S. tried repatriation recently.  In 2005, companies were allowed to bring back foreign source profits at a tax discount.  Rather than having to pay the difference between the foreign tax rate and the U.S. tax rate of 35 percent (tied for highest in the developed world), the companies instead could pay a de facto repatriation tax rate of 5.25% to the IRS–a bargain in most cases.  Over $300 billion was repatriated that year under this arrangement.  Given the relative size of overseas profits accumulated today, it's reasonable that this number could be twice as high this time.

Why should Congress adopt another round of repatriation?  American companies would respond to the low-tax repatriation offer and bring money from foreign accounts back to the United States.  This could be substantial–as high as several percentage points of GDP.  Best of all, this money doesn't come from the Federal Reserve (so it's not inflationary), and it isn't spent by Congress (like in a stimulus package).  It's almost literally money falling out of the sky.
The $500 billion-$1 trillion that would return to the United States would then be available to be deployed.  This money could be used to create jobs and invest in America.
What type of things could companies do with this money?  All money is fungible, so it's impossible to say with any precision what companies would do with the repatriated money.  Some will save the money as cash, to be deployed later.  Some will use the money to invest in new plant and equipment.  Some will create jobs.  Some will return value to shareholders in the form of stock buybacks or dividends.  Some will contribute to pension accounts.  The point is, this money belongs to these companies, and it's foolish to have a double taxation regime that prevents them from bringing this money back to America.
Isn't this a big tax cut for Wall Street and other big firms?  Actually, the government received a tax windfall in 2005.  Because this money was never going to be coming back here under the double taxation regime, corporations who then had a one-year incentive to bring back money ended up paying the 5.25% rate voluntarily (as opposed to paying nothing indefinitely).  The federal government received a tax windfall of $18 billion from this voluntary action.  This doesn't count the taxes paid once the deployed repatriated money started to be used.  For example, it doesn't count the income tax paid by a job created from repatriation money, but this is also obviously a benefit.
Why not do territoriality instead?  Smart tax politics often is about having simultaneous projects working toward the same goal.  For example, a goal is to eliminate the double taxation of investment.  Toward this end, conservatives push expansion of IRAs, 401(k)s, and other tax-advantaged accounts.  At the same time, though, we also push for a 0% tax rate on capital gains and dividends.  It's the same thing here.
Territoriality is a one-year fix that retroactively gives money close to territorial treatment.  Ideally, this should happen every year, and the whole system should switch over to a territorial one.  The perfect is not the enemy of the good.