I have seen so many sentences with "on" endings, example:The show must go on.
Can someone explain it to me, please
"go on" and 'grow up' are Phrasal Verbs.
The show must go on.
Expressions like "go on" are called VERBAL IDIOMS.
There are a huge number of verbal idioms in English and many of them contain prepositions like "on". For example:
Do you think this will ever catch on?
How are Ed and Kim getting on?
We call words like "on" in those examples and yours intransitive prepositions because they do not require an object, as in "Ed is sitting on the bench". If you drop the word "on" in that example, the sentence becomes ungrammatical.
You will sometimes hear verbal idioms wrongly called phrasal verbs. Ignore that term, it's rubbish - there is no such thing since. "Go on" is not a verb but a verb+preposition, two separate constituents.