Each commit should build and pass tests, yes. When I say "partial commits", I don't mean that the commits are arbitrary - each commit should be as small as possible to implement a specific fix/feature. I've also heard it described as the smallest unit that you may want to revert.
For example, if you are working on something, but it requires adding an API to some module, then the first commit 1 is to add the new API (+ tests), and the second commit is the new code that uses that API.
Unfortunately many developers I have worked with would just combine these (and more) into a single commit (because they are part of the same work task). However this makes review, bisect, blame and revert harder (if you need to revert commit 2, you don't want to also revert the API you added if that was tested and bug-free).
For example, if you are working on something, but it requires adding an API to some module, then the first commit 1 is to add the new API (+ tests), and the second commit is the new code that uses that API.
Unfortunately many developers I have worked with would just combine these (and more) into a single commit (because they are part of the same work task). However this makes review, bisect, blame and revert harder (if you need to revert commit 2, you don't want to also revert the API you added if that was tested and bug-free).