Source: CoinMarketCap
In the Wired article, they cite the fact that all Monero transactions are completely anonymous and untraceable. This achieved via a number of mechanisms that address vulnerabilities in Bitcoin's protocol. For example, wallet balances are obscured in Monero using so-called "stealth addresses." It has a feature known as "ring signatures" which essentially mixes up the transactions of many users at once automatically to make a forensic analysis of money flows impossible. It also hides the amount of each transaction from view. Wired concludes, "all of that makes Monero a significant upgrade for a cryptocurrency user’s financial privacy." People transacting in Monero can then change it back to either Bitcoin or to dollars (or other currency) via a number of online cryptocurrency exchanges.
Of course, having complete anonymity and opacity is valued by black market denizens, but is frowned upon by regulators and law enforcement. If the only perceived usage of something like Monero is for illegal or questionable activity, then its widespread use may be dampered. Indeed, Bitcoin used to be used primarily for black markets and gambling, but has since evolved in to a much more general use currency with very little illegal activity going through its network.