To uptight people, nonsensities are dismissed (usually with a hoity-toity British accent) as rubbish and not worthy of their intelligence, time and attention.
To people who use it playfully to refer to themselves or something they like, there is an element of fondness or self-deprecation present.
"Nonsensities" is a word more nonsensical than "nonsense" because it has twice the number of syllables, and more nonsensical than "nonsensicality" because it is (surprisingly) unlisted on several major online dictionaries (despite returning more than 10,000 Google search hits) and therefore officially unrecognised as a legitimate word and truly regarded as nonsensical.
It is usually used in its plural form, because "nonsensity" is not nonsensical enough. Contrast with the word "niceties".
But don't take my word for any of this, I am merely spewing nonsensities.