Unit Economics is a neat way to look at the fundamental economics of a business. A sanity check. It starts with defining a "unit". A "unit" could be a product sold or a customer acquired depending on the kind of business and business model. Unit economics would then describe how much value is created from this "unit".
Unit economics help you understand how much has to be given to perform a unit transaction that is core to the business. Especially when analysing a business, unit economics provide a quick way to check the feasibility of the business. It would be quite clear if an insane amount of money has to be put into for acquiring one customer. Or if the charges on logistics were eating up too much of the margins.
The unit economics and it's various components can be projected out in the future. This will give you a fair idea as to how the business would have to perform to stay solvent. Whether that is realistic or not is another question. Comparing figures in a per-unit basis eliminates the possibility of comparing different things all together. We do not want to compare apples to oranges.
An example of a unit economics for a restaurant would look like this. From a basic sense, a restaurant cooks food for their customers with a marked up price to earn a profit for the product(the meal) and service. So the margins of a restaurant meal would be the difference between the price of the meal and the cost that it took for the restaurant to make it. The cost can then be broken down into the hourly wage of the workers, the cost of running a kitchen, the cost of the ingredients etc. This would give us an idea as to how much would have to be spend and what each dish has to be priced to obtain a margin that would justify running a restaurant business.