Cats wagging their tails have many meanings, such as:

It means nervousness or excitement. If two cats are confronting each other and lower their ears to pay careful attention to each other's every move, they will wag their tails vigorously from left to right, indicating that they are in a nervous or excited state, and a fight may break out at any time.

Indicates impatience. When a cat is resting and is disturbed, the cat will shake its tail rapidly to express impatience.

It means you are in a good mood. When a cat voluntarily sleeps in a person's arms, its tail will swing wildly and slowly, indicating that it is in a good mood.

In addition, cats wagging their tails can also express friendliness, goodwill, curiosity about something, and intention to attack.