Here are two very simple but common use cases.
Each characteristic is tied to the product itself, e.g. a shoe cannot be both Nike and Adidas. Also, all products in a cart may not have the same characteristic, e.g. I can buy sweet and salty desserts in the same order.
You could use Classifications to solve this, if you track the SKU as your "Product" name, but let's say you don't.
To be able to report on sales per characteristic, you would use a Merchandising eVar to track that characteristic. Then, you'd be able to run a report per characteristic, e.g. all orders and revenue per Product Brand.
There are other use cases for Merchandising eVars, but these 2 above should be enough to get you started on learning how to use this feature.
We use merchandising evars when we want to allocate credits at product level. A very simple example which is given even in adobe docs is - Say a regular eVar captures search term.
If you search for item A, go to product A page (price $50), add it to cart.
Then search for item B, go to product B page ($100). add it to cart.
Then you go to cart and complete the purchase. In such case, for a total revenue of $150, a regular eVar with most recent setting would have the value of item B which would get all the credit (since it is the last value which populates it). But since 'item A' also had some role to play in final purchase, it is necessary to allocate credit product wise.
If we enable merchandising for the eVar, item A would get credit for $50 and item B would get credit for $100.