LTE-Advanced would mean faster data transfers -- about twice that of LTE. However, Apple has never been one to jump into bleeding-edge technology, so the rumor's veracity seems questionable. Remember that the first iPhone didn't launch with 3G, and also how long it took Apple to embrace LTE?
In addition, LTE-Advanced isn't widely available. LTE-Advanced hit on SK Telecom's South Korean network last week, with the carrier claiming it was the first to market.
U.S. carriers have plans, though, with Verizon Wireless stating that pilot programs would be launching in the next few months.
Notably, the carrier said that the new speeds would be available on current Galaxy S4s with a small ROM update. It's not clear if the speed achievable with this update would equal Samsung's dedicated handset.
That new handset, Samsung's new Galaxy S4 with LTE-Advanced built-in is dubbed the Samsung Galaxy S4 LTE-A.