French roots for the word exhort mean "thoroughly encourage," so to exhort is to fill up with encouragement! "When he heard the crowd exhort him with stomping and cheers, he knew that he could finish the marathon."
Some synonyms for exhort include stimulate, excite, and urge on. Words and shouts can exhort, and this is especially true when the recipient of those chants fears coming up short with an effort. Exhortations may make the difference between winning or losing and marching on or giving up. A sergeant might exhort his troops after a defeat just as a dad can exhort his daughter after a missed note during a piano recital.