Basically if someone can steal your password, they often can get into your system and do a lot of damage.
A quick review: authentication “factors” involve who you are, what you know, and what you have. A one-factor authentication technique involves just one of these three things: a key to your front door involves what you have, a password involves what you know. We can bolster the strength of any of these “factors” by requiring longer passwords or better designed keys and key locks, but you only have one thing to bypass to get into the system.
For “two factor” authentication to work, it involves two of these three factors: routinely it involves “what you have” and “what you know.” So your ATM card is a two-factor system: you must first present your ATM card, then enter your password PIN.
What makes two factor authentication more powerful is that now you have two systems (working on concert) to bypass. This also allows you to weaken one factor if the other factor must also be present–such as an ATM PIN which is an easily guessable 4 to 6 digit number.
The nice thing about cell phones is that it easily allows us to distribute software that allows your cell phone to participate in the login process: making “what you have” your cell phone as part of the login process.
And there are a number of applications out there which can be used as part of a two-factor authentication process, such as Google Authenticator, which implements TOTP and HOTP one-time passwords. It should also be relatively easy to implement your own one-time password application, though ideally unless you know what you’re doing, just download and drop in the libraries from someone else’s implementation.