Short answer: Drain cleaning clears blockages from grease, soap, hair, and debris, and the right approach depends on where the clog is: a single fixture, the kitchen, the bathroom, the main line, or the sewer connection.
Drains clog for different reasons depending on where they are. Kitchen sinks deal with grease and food debris. Bathroom drains deal with hair and soap scum. Main lines and sewer connections can involve tree roots or long-term buildup that a single fixture never sees.
The pages below separate drain cleaning by where the problem is happening, since the cause — and the right tool for clearing it — tends to be different in each case.