Horton being an Elephant is the only one able to hear the Who's due to his big ears.
He talks to the Mayor of Whoville, telling Horton that everytime the speck is moved it causes changes to Whoville (If the speck is covered, then Whoville goes into nighttime)
Horton tries to get the speck to a spot on a mountain so that the Who's can live in peace. Since no one else can hear the Who's, everyone in the Jungle thinks he's crazy.
Horton convinces the Who's to help him. All the Who's in Whoville make as much noise as possible and are able to make everyone hear the Who's and believe Horton.
The Mayor's Son finally talks.