Remember that in atomic chess, the kings are allowed to reside on adjacent squares. This is often a pivotal issue in endgames. The weaker side often seeks to connect kings in order to avoid mate, at least temporarily. For example, consider:
8/8/4Q3/1K6/8/3k4/8/8 b
Black to Move and Draw
Black draws by playing 1. ... Kc4. Now the Black king cannot be taken because the White king would explode too. Wherever the White king moves, the Black king follows like a shadow.
It should be noted that connected kings doesn't grant the weaker side an automatic draw. If the stronger side has enough material, he may be able to pry the kings apart. For example, consider:
8/8/8/8/8/8/QkQ5/K7 w
White to Move and Win
White separates the kings by playing 1. Qcb1 Kc3 2. Qeither-b2+, and now the win is easy.
Also, if the weaker side has material besides his king, the stronger side may force him to move adjacent to his material and then kill the king by indirect explosion, all while both kings are still connected. This is one of the great ironies of atomic chess, that having extra material can often be a liability. For example, consider:
8/8/3Q4/8/3pk3/3K4/8/8 w
White to Move and Win
White wins by playing 1. Kc2 and now if 1. ... Kd3 then 2. Qxd4##. So, Black cannot follow the White king and is forced to play 1. ... Kf3 or 1. ... Kf5 after which he will be mated quite quickly.
Another irony of atomic chess is that in many endgames the stronger side tries to connect kings. This is often done to avoid an immediate draw and the intent is to pry apart the kings later when it is safe to do so. For example, consider:
8/8/5P2/R6P/p1k1p3/P3P3/3r4/2K5 w
White to Move
Here White should play Rc5+ forcing the Black king closer to the White king so that White can connect kings. White will then have time to queen his pawns and then he will count on his superior material to win the game. Without connecting kings, Black will achieve a draw with perpetual check (Rc2+ etc.)