With infinite, do they mean actually infinite, or the infinite from the PC version where the map is huge, but beyond the boundaries blocks don't have barriers and you can't build there? I'm guessing the same as PC?
The world is randomly generated and saved the furthur out you go. From the Minecraft Wiki about the PC version:
are somewhat infinitely big - They are made up of chunks; this means that as the player explores the map distant chunks are generated automatically, leading to theoretically infinite maps. In practice, technical reasons (the limits of 32-bit math) force the maximum map size, including the Far Lands, to be around 9.3 million times the surface area of Earth , which comes out to about 4.7 quadrillion km2 (The hard limit where chunks are overwritten is at X/Z of ±34,359,738,368, making the world at most 68,719,476,736 meters wide and long, which is about 4,722,366,482,869,645 km2. When compared to Earth's total surface area, 510,072,000 km2, this works out to be about 9,258,235 times that). Whilst the horizontal planes of the maps are vast in size, the vertical plane remains at a fixed (soft limit) 256-block height .
So not really infinite but 9.3Million times the surface area of earth is pretty damn huge. Might as well say infinite as no one will waste their time exploring all of it.... at least I hope not... PS4 version might be something like just 100 Earths and it would be ok for them to say infinite since players would never see it all. Not to mention each new game is a completely different world. I wouldn't be suprised if the numbers were similar to the PC version, though.