To cajole someone is to persuade them by using insincere compliments or promises. If you say "Please, pretty-please, I'll be your best friend," when asking for a stick of gum, you are cajoling the gum holder.
The origin of this word is probably a blend of two French words meaning "to chatter like a jaybird" and "to lure into a cage." When you cajole that guy into lending you some money, picture him as the bird going into the cage. In fact, the word cajole may be associated with another French word meaning "to put in jail."