I looked it up the other day.
As best as I can tell, it's succeeding because
1) it's more single focused than its competitors - it's about peer payments more than grocery store/etc payments.
2) it's got financial backing of Paypal (owner)
3) it's social (not sure why this is an appeal, but articles seem to claim it is)
4) it's built a network affect with millenials already (not sure how. awesome marketing at "welcome to college get your credit cards here" day?)
Google Wallet/etc. are android, and Apple pay is android, but what's cross platform? Venmo apparently. For now.
Most of this is pieced together/speculated after reading a couple articles and searching reddit for mentions of venmo alongside google wallet.