"Irlol" stands for "I Really Laughed Out Loud." Since people tend to send "lol" whenever they find something funny rather than when they actually have laughed out loud, irlol is for those time when someone has in real life, actually laughed aloud.
An extensive and more assuring phrase than the traditional lol. Translates to
I
Am
Really
Laughing
Out
Loud
Adopted after lol began to be used as a way of politely keeping up the flow of an online conversation instead of expressing sincere laughter.
Means that the person is literally, as they type the phrase, laughing out loud, usually uncontrollably.