Not the same as being humble or modest, "self-deprecation" is literally to deprecate -- "to lessen in price or estimated value; to lower the worth of; to represent as of little value or claim to esteem; to undervalue" -- oneself before others. It means putting yourself down, denigrating yourself, insulting your own appearance, personality, history, position, occupation, or life for other people to see and hear.
Generally, you have one of two objectives. One is fishing for complements, putting yourself down so that other people will pick you up out of misguided sympathy. This is a form of narcissism. The other is beating the listener to the punch, insulting yourself so that you don't have to hear someone else do it instead. This is a form of paranoia.
Self-deprecation is responding to "You did a good job" with "No, I suck." Modesty is responding with "No, that person did much better." Humility is responding with "Thank you" and nothing more.