I believe the app at least used to be just that - an app that popped up from time to time asking you to complete a short questionnaire about your behaviours. So it shouldn't really impact your internet usage. Basically, you're joining a big panel, and whenever Google's advertising sales team need the answer to something they don't already know, they can ask the panel and get a robust response from panellists that can inform them.
To be clear, this is for advertising sales, and that alone. Talk of "representing your community" just means that they're short of people in your zipcode/sex/age/ethnicity to make a representative sample.
I don't believe that it's an app that monitors in the background every single site you visit - there are such apps - but I'd definitely read the small print. In January, Facebook was caught by Apple using such an app to read just about everything on people's phones using an app called Facebook Research. They paid participants - including teens - $20 a month to be included. Apple pulled the plug on that when they found out. But I don't think this is what Google is doing. (Facebook incidentally has recently launched a new version of its app which is closer to Google's although it still measure things like how long you spend in apps that are not made by Facebook - they want to know why your spending more time on Snapchat than Instagram or whatever).
I'd also seek a clarification on that "$479 ... per year" because $479 seems to be a $141 install bonus plus 52 weeks x $6.50. But do they give you another install bonus the following year? If not, then your annual amount would drop down a fair bit. Maybe a new TV in year one, but not in year two.
Also it says "up to" $141, and "can" translate to $479. I suspect that the amount you get depends on how hard it is to recruit into your demographic. But maybe I'm being cynical. I've worked in market research, although I've never maintained a panel like this, and rewarding panellists to keep them on board is standard practice.
To be clear, I've previously used a version of this app some years ago, although I didn't make more than a few pounds that I was only able to use in the Google Play Store. The rewards they're offering you are bigger. I did however once attend a Google focus group to answer questions on using work email on a personal Android phone. But that was completely different and I got cash!
Adam