When someone supplicates, they ask for something in a very humble way, like they are begging for it.
Supplicating is usually a serious and desperate thing to do.
Examples:
She supplicates for forgiveness.
He supplicates for help.
The dog supplicates for a treat.
The cat supplicates for more food, even though it just ate.
He supplicates for a second chance, even though he knows he made a mistake.
She supplicates for the pain to go away.