You should be told what to do. Your manager is both asking you to work on something ("please log your hours") but you don't know what he expects you to work on.
Generally, you would always be doing "something" for the company (otherwise, why is it employing you?). There are cases where there's not much to do (e.g. a helpdesk with no calls), in this case it seems that your company is keeping you awaiting a project which is going to be assigned "shortly".
However, the expectation should be clear on what he would like you to do. Some examples include:
- See if you can help in any way the guys from team B or team C.
- Watch a conference, read a paper about X
- Try to learn a new language/technology
- Do some maintenance on <different project> (e.g. improve the documentation of your previous project, which was not as good as it could have been)
- Investigate that bug which haunted you on a previous project (like an odd db deadlock) and was worked around badly, since you never figured out why (it may help so that in the future you do not fail for the same trap)
- Think on a project that could be useful to the company and try developing it (for example, crating a commit hook that checks your internal programming style)
As you see, these are things that would give certain value to the company (playing cards with your colleague would probably not make your company too happy). These would generally be short tasks, which don't take much time (given that you may need to stop it whenever you get a new project assigned). I would recommend you to take advantage of this time to do some self-training, which is usually something for which there's never time.
Of course, once you figure out what to do, you would then log the hours appropriately, either as specific tasks (e.g. learning Rust, browsing stackoverflow) or generic ones (e.g. trainings).
I would recommend you to ask your manager what he expects you to do, and maybe suggest a list of the above possibilities (or make up your mind and actually a specific proposal "since we still don't have a project to do, I thought I could do XYZ which we may find useful later, is it ok?").