The word "hacker" describes people who find weaknesses in an established computer system. That use to sound positive, but the contextual definition is rarely used today. Many have long debated that those who break into computer system and exploiting them should be called cracker to distinguish black hat "hackers" from white hat hackers. Anyway, as popular definition suggests, hackers violate computer system for personal, monetary and malicious gains.
Black hat hackers/crackers are seen as online criminals who victimize people's online accounts and illegally eliciting personal information, social security number, and credit card details. They can also bring down the entire system, destroy data, and populate it with malicious information.
They infiltrate the system through different methods. The most popular would be something ordinary people do: guess password by taking into consideration some clues from the owner of the system or an account. More sophisticated methods include keylogging, primary email address hack, social engineering, and cookie stealing.
Meanwhile, white hat hackers also find weaknesses in an established computer system but with a different purpose. Instead of performing malicious activities, they identify weaknesses in the system so that it can be improved by the owner before it is discovered and breached by others. The term "white hat" is an internet slang that refers to ethical practice. (White hat and black hat is also used in SEO.)
White hat hackers do this as a hobby and offer their services for free, but there are also those who become consultants of different companies and paid for the job they do. Many white hat hackers used to be black hat hackers.