What is the main idea/purpose of endorsements and sponsorships, and what two facts would you show that endorsements influence people?

In economic terms, there can be two purposes for having these things.  You can do them to try to increase the demand for your product, or you can do them to try to decrease what is called the "elasticity" of demand for your product.

Once thing that determines demand for a product is consumer tastes.  If you can get someone popular to endorse your product, your product may become "cooler" and more people will want it.

Elasticity of demand is a measure of whether people will keep buying your product if its price goes up.  You want demand to be inelastic because that means when you raise the prices, you make more money (people still buy your stuff).  To make demand be inelastic, you have to convince people that your product is way better than other similar things.  So you have someone endorse it to try to create that idea.