A more thorough explanation:

Definition: When someone's behavior is annoying and harassing without any reasonable or probable cause or excuse.

Examples:

• A neighbor who constantly complains about the smallest things, like the sound of your children playing, is being vexatious.
• An ex-partner who sends you multiple messages and calls you repeatedly, even after you have asked them to stop, is engaging in vexatious behavior.

These examples illustrate the definition of vexatious because in both cases, the behavior is without any reasonable or probable cause or excuse. The neighbor and ex-partner are being annoying and harassing without any valid reason, making their behavior vexatious.