Interest means that the money on the accounts belongs to you, regardless of who's name is the account titled to. For example, if you give money to someone (non-US person, say, trying to avoid FBAR requirements) and that person puts it in his account but will give you money whenever you ask for it - you have interest in that account. This is in order for people not to avoid FBAR requirements by putting their money into someone's else accounts.
Signature Authority means that although the account is not in your name, and the money on it is not your money - you have the right to access that account and perform operations on it. This usually happens when people are employees of a company and have signature authority over the company's accounts, but it is also frequently the case for people having signature authority over the accounts that belong to their family members (for example - your parents are not US persons, but they gave you access to their account because they don't know how to work with the bank and you do - you have signature authority over the account).
If you have your own account - you have both interest in it and signature authority over it.