No, the developers didn't figure out a way to integrate the iPhone with a DeLorean or power it with a Mr. Fusion. What the app does provide is maps with 750 points of interest, as well as 1,500 photos and 150 audio guides that are bundled into the app so that you don't have to rely on a cell phone signal to take advantage of them. The tour information is provided by qualified Blue Badge guides, so you're getting accurate and interesting information.
The time travel bit comes in with maps of London from 1862, 1830, 1799, and 1746. The base Time Travel eXplorer - London app (US$2.99) includes a demo map from 1862, and you can do in-app purchases of the old maps in their entirety for a few bucks per map. Alternatively, you can buy a Pro version of TTX ($8.99) that includes all of the maps.