To plead with someone is to try to convince them to see it your way. Your kids may plead with you to let them go on the super-huge outrageous roller coaster built in 1968, but you know better.
The term plead comes from the word plea, which is from the legal system, where lawyers make a plea to the court and argue a case for their client. To plead is to ask for something from someone, often on the verge of begging. You may plead with the phone company to give an appointment time that spans only three hours, but, regardless of your pleading, they will make you wait eight hours for the technician to finally show.