The exact meaning of suppress can depend upon its context. For example:
"suppressed the revolution" — to stop others from doing something by force
"suppressed a smile" — kept something from happening
"suppressed the story" — kept news from spreading
"suppressed her fear" — controlled an emotion
"suppressed the memory" — avoided thinking about (perhaps even removed from conscious memory)
But Barb Wiggin and Harold Crosby closed their eyes; Harold did not look well—he seemed to be suppressing vomit, and his face took on the lime-green shade of the grass at the feet of Christ's disciples, who loomed over him.
There are no more uses of "suppress" in A Prayer for Owen Meany.