A miracle was an event which could not be explained by physical laws or scientific principles.
In 2258 of the alternate reality, Darwin proclaimed the USS Enterprise's stabilization over Earth's atmosphere to be a miracle, to which a skeptical Spock proclaimed that there were no such things. (Star Trek Into Darkness)
In 2268, Spock's brain was surgically removed yet he remained alive. According to Doctor Leonard McCoy, it was the greatest technical job he had ever seen. Every nerve ending in the brain had been neatly sealed; nothing ripped nor torn, and no bleeding, which he considered a medical miracle. (TOS: "Spock's Brain")