The tooltip is simply unclear.  It increases growth when you are using the "Produce Growth" build option in your city.  That's why it doesn't look like it's doing anything - after all, if you're building the festival, you're not producing growth!

The problem is that the tooltips are not all the same.  In the screenshot above it's showing you what you would get with your current status, which is 0% growth, and relies on you to already know that it only applies a growth bonus when you're Producing Growth.  This is not a good assumption.  You should have all the information you need in the tooltip in the build menu.  There are several cases where different tooltips for the same thing do not match each other, or leave out information.