The security of your online accounts are becoming more and more important everyday. Previously an email address was only used to check and respond to emails. Now, something like a gmail address is tied to your phone, email, calendar, contacts and most importantly of all, your credit card information. All of this is protected only by your password. The most popular additional layer of security you can get with most of the providers is two factor authentication.
Two factor authentication uses another layer of security in addition to your standard password. You can use a phone call, sms message or even an email as the second verification method. Basically the only way to access your account is to be able to pass both verification steps. For convenience most users set two factor authentication to send an sms code.
In practice, whenever you sign in or conduct an important transaction, after entering your password you will be asked to enter a code sent using whichever second verification method you selected. The code is usually a six digit code. Once entered you are then logged in. You will also be presented with an option to not be asked for a code again for that specific browser. Use this only if it is your computer which you use regularly.
This makes it much harder for a malicious attack or hack attempt without your knowledge. A successful hack will now require both your password and a secondary device connected to your two factor authentication.