Home Tie-Ins With Infinite Crisis
The Kingdom was the sequel to Kingdom Come, a huge, apocalyptic vision of the future of the DCU's heroes. While I am not going to be dealing with Kingdom Come here, I recommend visiting Jess Nevin's site which annotates it along with others.
As impressive as Kingdom Come was, it would be hard to follow it up. From the point of view of Infinite Crisis, The Kingdom is notable only as being the first in continuity appearance of the Earth-Two Superman (Kal-L) since Crisis On Infinite Earths.
With the help of the older versions of themselves, Superman, Batman and Wonder Woman defeat a misguided villain called Gog. In doing so, however, they discover Hypertime which, in essence, allows all stories that have ever taken place in the DC Universe - whether pre- or post-COIE, in the Elseworlds imprint, or even those that have been ret-conned out of existence - to have taken place. A fuller explanation of the concept can be found at this Wikipedia page.
If Hypertime allows for all stories to have happened, then the original COIE must have taken place, leaving Kal-L (along with Superboy-Prime, Lois Lane and Alex Luthor) in their heaven. It is in this heaven that the readers encounter Kal-L who, at the very start of issue #1 of The Kingdom, is seen trying to break through an invisible barrier that imprisons him. At the end of issue #2, after the heroes have discovered the existence of Hypertime and Kal-L has made eye-contact with Superman, he realises that there may be a way out.
Hypertime itself was later ret-conned out of the DCU, though it was briefly mentioned in week twenty-seven of 52 where Skeets refers to Waverider as the "seer of Hypertime." With the concept gone from the DCU, Infinite Crisis #1 becomes the first in-continuity appearance of Kal-L since COIE.
It's worth mentioning, however, that at the end of 52, a new multiverse was created which contained, among other, Earth-22 which appears identical to the future that Kingdom Come portrayed. If the events occured on Earth-22 as depicted in Kingdom Come, then it's possible that in the history of Earth-22 Hypertime still exists...