Nonsense is stuff that sounds like language but doesn't have any meaning, like the phrase higgledy-piggledy-po, or fwumphy-doo. The most famous nonsense poem is Lewis Carroll's "Jabberwocky."
Nonsense means exactly what it sounds like: not containing a lick of sense. Nonsense words are made up. But sometimes if you say something in a really confusing way, people will say you're speaking nonsense: even though you're using normal words, you don't make any sense. Sometimes people will dismiss ideas that they don't like by calling them nonsense, but you might know better. Little household knick-knacks that have no purpose are also called nonsense.