This is a very common observation. If you click on the question mark by the DNA Circles section, there is a page with a number of FAQs. One is "What is a New Ancestor Discovery?" (which people are starting to abbreviate as NAD). It describes three scenarios: you're a direct descendant of the person, or you're related through marriage or a collateral line, or you have many common ancestors.

I wish we could post direct links to the FAQs.