Meaninglessness is a quality of being hollow or lacking any significance. The meaninglessness of your sister's apology was obvious from the way she rolled her eyes.
Anything that lacks true meaning has the characteristic of meaninglessness. Some philosophers have written extensively about the meaninglessness of life, while your best friend might complain frequently about the meaninglessness of algebra. Both statements imply a lack of significance. You can also use this noun for things that are unintelligible to you: "I don't read French, so I was frustrated by the meaninglessness of the words on the menu at that new café."