Many people believe that animals or people who have seziures will be more prone to having a seizure during certain phases of the moon. This Wikipedia article describes something called the “Lunar Effect”. A recent study looked at how many seizures animals had during different phases of the moon. You can read the abstract of the article here.
The study looked at 211 dogs and cats over a period of eight years. Each of these animals had idiopathic epilepsy (which means they have seizures, but the cause is unknown). The date of each seizure was documented. Then, they looked at whether the seizure happened during a full moon, new moon, or any other particular lunar phase.
The study concluded that there was no correlation at all between the phase of the moon and the number of seizures that an animal had. So, it looks like this is just urban legend!