Meetings of this sort are pretty standard, but my experience is they're usually at a later stage of the process, like a second visit. Deans don't like to waste the time if the candidate doesn't pass muster of the faculty.
For better or worse, the Dean and the Provost carry a very big stick. Your recruitment can be halted in a split second if one of them decides that way. The way it goes is that search committees make recommendations to Chairs and Deans. At intermediate stages, they will advance a handful of applicants for consideration. If the Dean or higher up says to the Chair "I would prefer if you don't hire that candidate" that's usually a done deal.
In subtler cases, they can come up with "extra" resources to make your package a bit more exciting if they feel you're worth it, such as bumping the size of your startup package with discretionary funds.
If the Deans or other high level officers want to meet with you at an early stage, that's could be just due diligence, providing a reality check, but it could be almost anything. Could be a young department or chair, and the Dean feels the need to keep an eye on the process. It could also be an indication that the search has advanced to a fairly late stage, and they want to make a hire quickly. It could also mean that these officers take a very active role in the management of their faculty, which could be a good thing. It could mean that they take a very active interest in a campus with a family-like leadership style. It could also mean that you're being considered for a very strategic hire and that they have a key interest in making sure just the right person is brought in to advance their programs.
There's also the possibility that you're a desirable candidate, and they want to impress you by showing high-level interest in your recruitment right from the start.
It's very hard to know exactly why they're directly involved without asking them.
In any case, be responsive to their questions. Use earlier meetings with other faculty to try to get a feel for the slot you're being recruited for, and in your big meetings, be the person they're looking for.