Yesterday's Dota 2 update had a few additions: a new Treasury, a Tournaments area in the Watch section, a preload of the Reborn Update (I'll leave it to Chris to explain the significance of that), and some items for those who bought a Compendium for The International 2015. But the headline feature was Dota Levels.
From now on, you'll have a badge on your Dota Profile that quantifies your Dota 2 accomplishments and experience: your Dota Level. You gain one Dota Level for every 100 Trophy Points, which, naturally, you get from trophies. Of course, different trophies are worth different amounts of trophy points, and the team plans to release more trophies in future so you'll always have something to chase.
For those who've been playing Dota 2 for hundreds of hours already, don't worry: you don't have to start from Level 1. Your current Level is based on trophies you've already won, and the Dota team has introduced two new trophies to make sure you're properly rewarded for the time you've put in.
The Experience Trophy has its own levelling system, gaining points each time you play a match, and there's no limit to how many points it can give you so as long as you keep playing you'll keep levelling up. The Battle Veteran trophy is a commemorative trophy for those who earned Battle Points before this update, handing out an amount of Trophy Points based on their final Battle Point Level.