Dota 2 Reborn is an overhaul of Dota 2, and has been in testing since June. It's since exited that phase to become the main version of Dota 2. Anyone still playing the old version of the game will be unable to partake in matchmaking, which is only available with the Reborn update.
Reborn is a major update to Dota 2 that upgrade's the game's engine to Source 2. In addition to the engine upgrade, it features a new user interface, support for mods and custom game types, and more. The core game itself will remain unchanged, because messing with that sort of thing just pisses off the fans, many of whom play competitively.
Additionally, there's a new feature called Dota Levels that adds a badge to your profile, showcasing your accomplishments and experience. You earn these levels by accumulating Trophy Points, which you get from trophies. Trophies come in varying forms, with different points for each. For every 100 Trophy Points, you gain a single level.
Players who've been playing the game for a while won't have to start from level 1, because the level system is retroactive and takes into account all of your existing trophies.
In addition, there is an Experience Trophy that features its own leveling system. You can level it up by playing matches. There's no limit to how many times you can level it up.
The official Dota 2 site has a breakdown of how the levels and trophies systems work.
