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.
You can turn GPS tracking and the "time travel mode" on or off. With both turned on, it's possible to see your location on a map of London, then use a slider at the bottom of the map to dissolve seamlessly into the maps of the past. It's fascinating to see how some locations in London have changed drastically over the years, while others have remained untouched. On the present-day maps, there are icons to show the locations of Underground stations, restaurants, and other amenities, as well as pinpoints for historical points of interest.
The app is functionally well-designed and easy to use, as would be expected in a product coded by London-based developer Michael Kaye. Kaye's design savvy and ability to create unique user interfaces first surfaced in a parenting app called BabyBubbles ($2.99), an early version of which won an Appsfire App Star award.