System wide ad blocker

As far as how your phone connects itself to the Internet, either by cellular or WiFi, you need to consider the basics. When your phone has an online connection, that 'link' is what feeds whatever apps are sending/receiving data. Your browser app, or Twitter app, or texting app, or whichever app are each using that same connection between your phone's radio and our beloved but increasingly nutty Internet.
A system-wide ad blocker is working as a content filter on that online connection and at a lower level of your phone's Android operating system, that's why it's typically a root required thing. An ad-blocking web browser extension works just on your web browser, only able to filter content coming into your browser.
So whether your phone is rooted or not, the issue is either adding ad-blocking to your phone's connectivity or to just your web browser. On a system level it's an overall matter, on a browser level it's just your web browser.

(And it should always be noted that as annoying as ads have become, content creators and developers need the revenue from selling ads. All the 'free' sites and services we're now addicted to need to be funded one way or another.)

 

Ad block plus works in browser only, and not supported by all browsers.

Ad-away is a system wide ad blocker (needs root). Works by changing low level tables. Doesn't slow anything down (if anything, can speed up). Open source. Highly Recommended. Not available from Google play (because it does not align with google's business interests). Get it from a safe source: https://f-droid.org