Example 1
Our company picnic will be held at Disneyland.
We don't know what kind of business this is, but it sounds awesome. We at Shmoop live for Space Mountain. In this example, the possessive adjective our modifies the noun company to specify whose company it is.
Example 2
Vanessa is a talented artist. Her sculpture of Danny DeVito tying his shoes recently sold for $3,000 at auction.
Here, we use the possessive adjective her to show that the sculpture belongs to Vanessa, and we use the possessive adjective his to show that the undoubtedly tiny shoes belong to Mr. DeVito.
Example 3
Your friend Brittany borrowed my blender to make peanut butter and durian fruit smoothies but never returned it. Can you give me her number?
In this example, your shows that Brittany is a friend that "belongs" to you, while my shows that the blender is yours as well. Her indicates that the digits you're after belong to Brittany the blender stealer.
You may not want that blender back after Brittany's blended all of that durian, though. While the fruit has a delicious, custardy, almond flavor, it smells like a mixture of sewage, onions, and turpentine. In fact, its smell is so noxious that it's been banned from several hotels and public transportation in Asia.