It implies a sense of pleading and desperation, like someone who is in a position of weakness or need.
Here are some examples of how "supplicate" might be used:
* The starving villagers supplicated the king for food.
* She supplicated her parents for permission to go to the party.
* He supplicated the gods for a miracle.
It's important to note that "supplicate" is a formal word that is not commonly used in everyday conversation. It's often used in writing or in situations where there is a significant power imbalance between the person supplicating and the person being supplicated.