Here's a polarizing question: is a phone a second factor, in the context of two-factor authentication? Fellow infosec pro @johnnysunshine tweeted the above last week, and sparked a lively debate.
Before answering the question, let's back up a bit and explain two-factor authentication (or 2fa). To borrow an analogy I first used two years ago: 10,000 years ago, Grog and Mag formed a secret club. To ensure new members of the club would be accepted, they came up with a secret phrase. Thus was born the first password. One day Narg overheard two members greeting one another and learned the secret phrase. Thus occurred the first password breach.
Passwords can be stolen though, whether through a server database breach, or via a phishing scam, or by keylogging malware that captures the password as you enter it into a webpage. If a password is the only thing protecting your account, then a stolen password lets an attacker pretend to be you. If the attacker knows the right password, the server or website has no way of knowing it's an impostor.
By adding a second factor - something you physically possess (an identification card, or a token generator, or - the crux of today's question - a phone), the bar for an attacker is raised. Individually, each factor might be relatively easy to defeat. Gaining access to both a password and a device at the same time though takes more effort, and is far less likely. Not impossible, but less likely.