First, let's get the boring stuff out of the way. A product video is a form of exposition – a demonstrative explanation. It explains what the product is by showing how it works, usually by stating a problem then offering a solution. Done.
Here's the interesting bit.
Before buying anything, customers (you and me included) prefer to get up close and inspect the goods; make sure everything's kosher. Ideally, you want to handle the product, use your own indisputable senses to make sure everything checks out. There's just something about holding an item that makes it seem more . . . real.
If you think about it, a Product Video (as much as is possible) fulfils this old familiar need. This is why so many use extreme close ups or macro shots. The studio camera becomes your eye, leaning right in, emulating the process of close visual inspection.
Sometimes, for the exact same reasons, the shots will be in Point of View (POV). You will even see hands using the product, the angle so framed as to make them seem like your own. This is a narrative technique (Hitchcock used it all the time). It brings the viewer into closer psychological proximity with the product.
A product is a lot more than its utility. It has curious psychological properties which are difficult to pin down. The point of a Product Video, then, is to bring a resonant, emotional, physical experience to the viewer. The exposition is important too. Only, remember, humans are often more swayed by how they feel toward a product than what they think about it.