Creating an Abstract Interface around DB Connection

I was reading this article on Unit Testing. It seems pretty straightforward, but there was a section that interested me and I wanted to see if someone could please provide an explanation or example of what this means. I think I understand it but maybe not well enough.

Write test cases that are independent of each other. For example, if a class depends on a database, do not write a case that interacts with the database to test the class. Instead, create an abstract interface around that database connection and implement that interface with a mock object.

What does it mean to:

1. create an abstract interface around the db connection?
2. then implement it with a mock object?

I am more questioning the first part (1) but if someone can explain both parts that would be helpful. Thanks.