A hint is an instruction to the optimizer
a code that tells a computer to perform a particular operation
Which means Oracle CBO must obey the hints and must perform particular operation. The latter is hard to define correctly and explain precisely because it involves the logic of the block-box (what Cost Based Optimizer is). Some of the operations are mentioned in the standard Oracle documentation, some of them scattered across different places, and there are exceptions as usual. I think I’ll list here these cases which could lead to “ignoring hints” with the links to documentation/blogs.