It mostly has to do with the legality of earning revenue without paying income tax, credibility, and additonal benefits of being a 501(c)(3).
As far as the IRS is concerned, if your organization is bringing in more than $5000 (gross, not net), it should be formally set up and SOMEONE should be filing with them. If you aren't set up as a 501(c)(3), then you are basically a business and should technically be filing a commercial return.
You might want to use "501" as the key word and search the Forum. There's lots of info posted and folks here are generally pretty helpful.
Of course, many, many PTOs and other such organization never do anything like this. They just operated in good faith (hopefully) and either don't know the rules or else just hope no one notices. And, frankly - it's not like the IRS is going to go on a big witch hunt for all the PTO's who make more than $5000.
I don't think you "have to" but the advantages include not paying most taxes associated with your earnings. Otherwise you are a money making organization like any other. There's a lot of smart, smart folks on this that can fill in the details...