In the list of characteristics of a good product owner, we have this far discussing those in informal situations - being engaged and involved. However, product ownership is also a lot about making decisions, and then I like the product owner to be decisive.
System development is a lot about making decisions. Even when we write code (and perhaps especially then) we make hundreds and thousands of micro-decisions. Some of them have mainly technical implications (make this design one class or two), but some of them form enterprise logic (what fields should I use when computing this if-conditional).
Sometimes these decisions grow a little bit larger, and we want to ask someone about what we should do. For example we might be writing a batch-file reader and wonder how we should handle if someone sends in the same file twice. Perhaps we consider saving some kind of file ID and a content hash to detect that situation. This might take a day or so to implement so most probably we will bring that up during the daily standup.
That standup is when the product owner can step in and make a huge difference. Of course the PO needs to be there (involved) and needs to care (engaged), but if she is she might make a huge difference by saying:
"Hold that thought. To me that seems like a separate story (Avoid duplicate file read). It is good enough if you implement this without that feature. if same file is sent twice, and we read it twice - then so be it. I make it new story and bring it up with the stakeholders."
Viola, within one minute the product owner have saved the team one day of coding, just by being decisive.
Product owner need also be able to take decisions at point blanc, even when there might not be enough information.
Team member: "I wonder, what shall we do about social security numbers for people with protected identity"
Product owner: "I do not know whether we have a case for supporting protected SSNs - need to check that up. Ignore that feature for now, if necessary I will add that as a new feature later."
This is just a few minute conversation, yet it saves the team hours of work by not loosing tempo.
Being decisive rules out product owners that "just want to investigate a little bit further before saying anything definitive" - such behaviour leaves the team floundering on what to do, whether they can proceed on the assumption or if they should wait.
Being decisive is a characteristic in a personal context, as is engaged. However it is more about making decisions rather than informal situations - so in that respect it is more related to being empowered.
Nevertheless, having a decisive product owner makes things so much easier to keep things rolling.