Internal laugh out loud. The laugh out loud you do when you don't actually laugh out loud. In reality this accounts for 99.99999% of actual lols. Often misunderstood by Apple fanboys to be related to Apple simply because of the i prefix. This misunderstanding in itself causes an ilol.
That cat video made me ilol. (Meaning I watched the cat video and thought it was mildly amusing but I made no physical sound, although I may have smiled.)