"Irreversible melting" means that something is being heated or warmed to the point where it liquefies, and this change cannot be reversed or undone. Once it has melted, it cannot go back to its original solid form. Full definition
Conservative estimates so far, projected irreversible melting in the course of a few centuries, depending on the temperature increase. (climatestate.com)
For example, the weakening of the THC under 1 degree of warming, a risk of collapse for 3 degrees, risk of irreversible melting of the Greenland Ice sheet at 2 degrees warming, sea level changes of 5 — 12 meters over several centuries, — these eventualities are debatable, and should certainly be viewed as the «adverse tail» of possible impacts. (realclimate.org)
This ice sheet is losing mass at a rather larger rate (around 220 cubic kilometres per year) and it will take only another 1 - 2 oC world warming to raise the summer melt zone to the top of the Greenland ice pack after which point, in my understanding, the ice sheet will go into irreversible melt. (realclimate.org)