He's noticing that his hands aren't shaking...
If you notice, Enzo pulls the cigarette pack and his hands are visibly shaking. He's terrified and can't get the lighter to spark.
Michael takes the lighter from Enzo, lights it on the first attempt and looks at his hands... not the lighter itself.
It's sort of spelled out in the script...
Outside the hospital is empty save for a nervous ENZO,
pacing back and forth brandishly the flowers as his only
weapon. MICHAEL exits the hospital and moves to him. They
both stand under a lamppost in the cold December night.
They are both frightened; MICHAEL gives ENZO a cigarette,
lights it. ENZO's hands are trembling, MICHAEL's are not.
..but the source novel tells us more.
Michael was touched. He was about to tell the young man to go away again, but then he thought, Why not let him stay? Two men in front of the hospital might scare off any of Sollozzo’s crew sent to do a job. One man almost certainly would not. He gave Enzo a cigarette and lit it for him.
They both stood under the lamppost in the cold December night. The yellow panes of the hospital, bisected by the greens of Christmas decorations, twinkled down on them. They had almost finished their cigarettes when a long low black car turned into 30th Street from Ninth Avenue and cruised toward them, very close to the curb. It almost stopped. Michael peered to see their faces inside, his body flinching involuntarily. The car seemed about to stop, then speeded forward. Somebody had recognized him.
Michael gave Enzo another cigarette and noticed that the baker’s hands were shaking. To his surprise his own hands were steady.
The Godfather - Mario Puzo