Just wondering how the level that you gain from battle points affects the game, if at all. Is it just an e-peen thing? Is it a match-making thing?
The only known difference would be that, each time you level up, you get a random item.
But yeah it can definitely be an "e-peen" thing, seeing as they're public, and you get more points for wins. With some thinking you can guess that the level 10 guy with 100 wins probably doesn't have as many losses (and subsequently higher e-peen) as the level 10 guy with 60 wins (because he has a lot of losses to make up for the difference in won games).
Profile levels have a few functions in Dota 2. They determine the tiers of items you are eligible to drop after a match, and for every level up, you will gain a guaranteed new cosmetic item. Certain queues are also enabled depending on your profile level, such as Ranked matchmaking which is enabled at level 13.