Hi Pam,
Yes, a Product is an object. It's a Non-Project Investment Object (NPIO) and typically part of an investment Portfolio.
The purpose of the Product object and the PPM features related to this object is to store and process key data for New Product Development (NPD) investments and to extract and analyze insights from this data (e.g. reporting). Many of the attributes and objects associated with Product instances are the same as those for Projects and other NPIOs (Team, Financial plans, etc).
Products can have hierarchical relationships with other parent and child investments for Financial rollup.
Establishing a hierarchical relationship with Project investments is one way that you can 'attach' a Project to a Product. There could be other ways to achieve this, so I will let other community members chime in about that....