The apostrophe is used to indicate missing letters relative to some standard English.
There are a number of situations where letters may be missing: There are several common contractions, such as I'm for I am, or don't for do not. There is also the use of the apostrophe in possessives (originally also a contraction, now just a rule).
There is also the use of apostrophes to indicate a particular contracted pronunciation of a word in a dialect. I this case the speaker has contracted
These people are going to tell you...
to "... are gonna ..." to
These people gon tell you...
This is typical of some rural American dialects. The author wants to indicate the dialect. The apostrophe hints that letters are missing, relative to the standard spelling and help the reader work out what is being said. In spoken English, the accent would also guide the hearer to expect this kind of contraction.
You will see various attempts by authors to write in an accent. Many accents and dialects have contractions compared to standard English. For more examples, look at JK Rowling's attempt at West Country English in What English is this? which is analysed in greater depth in an analysis of Hagrid's dialect