An eruption is a violent breaking out; an irruption is a violent breaking in. The discharge of lava from a volcano or of water from a geyser is an eruption. An invasion by an army is an irruption. In ecology, an irruption has the specialized meaning of an "increase," such as of the population of a country: "Improved health care and an increased birth rate resulted in an irruption during the past decade."
Dictionary of problem words and expressions. Harry Shaw. 1975.