Cats purr when you pet them primarily as a sign that they like the interaction and are content. Purring is a voluntary vocalization that cats produce with their mouth closed by creating a continuous vibration during inhaling and exhaling. When a cat purrs while being petted, it often means they feel safe, comfortable, and happy in that moment. Besides contentment, cats also purr for other reasons, such as:

• To seek attention or signal that they want more petting.
• As a self-soothing mechanism when they are anxious or stressed.
• To communicate greeting or affection.
• To help relieve pain or discomfort through the therapeutic vibrations of purring, which promote healing and bone growth.

In summary, when your cat purrs while you pet them, it is mostly a positive sign showing they enjoy the interaction and feel secure with you. However, purring can also serve as a coping mechanism in less positive situations, so it's important to consider the cat’s overall body language and context to understand the meaning fully.