This template function returns the current users cart, which is an Order Model.
You would get cart for the current user like this:
{% set cart = craft.commerce.carts.cart %}
which is the same as:
{% set cart = craft.commerce.getCarts().getCart()%}
You can now show the current customer their cart, and add things to this cart with forms in your templates.
Once a Cart is completed and turned into an Order, calling the function again will give your user a fresh new cart.